|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/01.07.21.2751.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Integrate[z^n E^(p z^2) Sin[b z^2]^m Cos[c z]^v, z] ==
2^(-1 - m - v) ((-z^(1 + n)) Binomial[m, m/2] Binomial[v, v/2]
ExpIntegralE[1/2 - n/2, (-p) z^2] (-1 + Mod[m, 2]) (-1 + Mod[v, 2]) +
(z^(1 + n) Binomial[v, v/2] (-1 + Mod[v, 2])
Sum[(-1)^k Binomial[m, k] ((-1)^m ((-2 I b k + I b m - p) z^2)^
((1/2) (-1 - n)) Gamma[(1 + n)/2, (-2 I b k + I b m - p) z^2] +
(((-I) b (-2 k + m) - p) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2,
((-I) b (-2 k + m) - p) z^2]), {k, 0, Floor[(1/2) (-1 + m)]}])/
I^m + Binomial[m, m/2] (-1 + Mod[m, 2])
Sum[E^((c^2 (-2 s + v)^2)/(4 p)) p^(-1 - n) Binomial[v, s]
(Sum[2^(-n + q) (I c (2 s - v))^(n - q) ((2 c s - c v + 2 I p z)^2/p)^
((1/2) (-1 - q)) (I c (-2 s + v) + 2 p z)^(1 + q) Binomial[n, q]
Gamma[(1 + q)/2, (2 c s - c v + 2 I p z)^2/(4 p)], {q, 0, n}] +
Sum[2^(-n + q) (I c (-2 s + v))^(n - q) ((c (-2 s + v) + 2 I p z)^2/
p)^((1/2) (-1 - q)) (I c (2 s - v) + 2 p z)^(1 + q)
Binomial[n, q] Gamma[(1 + q)/2, (c (-2 s + v) + 2 I p z)^2/(4 p)],
{q, 0, n}]), {s, 0, Floor[(1/2) (-1 + v)]}] -
Sum[((-1)^k Binomial[m, k] Binomial[v, s]
(E^(I m Pi + (c^2 (-2 s + v)^2)/(4 (I b (2 k - m) + p)))
Sqrt[I b (-2 k + m) + p] Sum[2^(-n + q) (I b (2 k - m) + p)^
(-(1/2) - n) (I c (-2 s + v))^(n - q)
(-((I (c (-2 s + v) + 2 (-2 b k + b m + I p) z)^2)/(2 b k - b m -
I p)))^((1/2) (-1 - q)) (I c (2 s - v) + 2 (2 I b k - I b m +
p) z)^(1 + q) Binomial[n, q] Gamma[(1 + q)/2,
-((I (c (-2 s + v) + 2 (-2 b k + b m + I p) z)^2)/(8 b k -
4 b m - 4 I p))], {q, 0, n}] +
E^((c^2 (-2 s + v)^2)/(4 (I b (-2 k + m) + p)))
Sqrt[2 I b k - I b m + p] Sum[(-2 I b k + I b m + p)^(-(1/2) - n)
(I c (s - v/2))^(n - q) ((I (2 c s - c v + 4 b k z - 2 b m z +
2 I p z)^2)/(2 b k - b m + I p))^((1/2) (-1 - q))
(I c (-2 s + v) + 2 (-2 I b k + I b m + p) z)^(1 + q)
Binomial[n, q] Gamma[(1 + q)/2, (I (2 c s - c v + 4 b k z -
2 b m z + 2 I p z)^2)/(8 b k - 4 b m + 4 I p)], {q, 0, n}] +
E^((c^2 (-2 s + v)^2)/(4 (I b (-2 k + m) + p)))
Sqrt[2 I b k - I b m + p] Sum[2^(-n + q) (-2 I b k + I b m + p)^
(-(1/2) - n) (I c (-2 s + v))^(n - q)
((I (-2 c s + c v + 4 b k z - 2 b m z + 2 I p z)^2)/
(2 b k - b m + I p))^((1/2) (-1 - q))
(I c (2 s - v) + 2 (-2 I b k + I b m + p) z)^(1 + q)
Binomial[n, q] Gamma[(1 + q)/2, (I (-2 c s + c v + 4 b k z -
2 b m z + 2 I p z)^2)/(8 b k - 4 b m + 4 I p)], {q, 0, n}] +
E^(I m Pi + (c^2 (-2 s + v)^2)/(4 (2 I b k - I b m + p)))
Sqrt[-2 I b k + I b m + p] Sum[(2 I b k - I b m + p)^(-(1/2) - n)
(I c (s - v/2))^(n - q) (-((I (2 c s - c v - 4 b k z + 2 b m z +
2 I p z)^2)/(2 b k - b m - I p)))^((1/2) (-1 - q))
(I c (-2 s + v) + 2 (2 I b k - I b m + p) z)^(1 + q)
Binomial[n, q] Gamma[(1 + q)/2, -((I (2 c s - c v - 4 b k z +
2 b m z + 2 I p z)^2)/(8 b k - 4 b m - 4 I p))],
{q, 0, n}]))/E^((1/2) I m Pi)/(Sqrt[I b (2 k - m) + p]
Sqrt[I b (-2 k + m) + p]), {s, 0, Floor[(1/2) (-1 + v)]},
{k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0 &&
Element[v, Integers] && v > 0 && Element[n, Integers] && n >= 0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "n"], SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SuperscriptBox["z", "2"]]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]], "m"], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["z", RowBox[List["1", "+", "n"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["ExpIntegralE", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"]]], ",", RowBox[List[RowBox[List["-", "p"]], " ", SuperscriptBox["z", "2"]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ImaginaryI]", RowBox[List["-", "m"]]], " ", SuperscriptBox["z", RowBox[List["1", "+", "n"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "2"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "n"]], "2"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "2"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "2"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "n"]], "2"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "2"]]]]], "]"]]]]]], ")"]]]]]]]], "+", RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", "p"]]]], " ", SuperscriptBox["p", RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"], "p"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]], "]"]]]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"], "p"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]], "]"]]]]]]]], ")"]]]]]]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "+", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", "p"]], ")"]]]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", "p"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "b", " ", "k"]], "+", RowBox[List["b", " ", "m"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]], "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "b", " ", "k"]], "+", RowBox[List["b", " ", "m"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["8", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "b", " ", "m"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "p"]]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List["s", "-", FractionBox["v", "2"]]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["8", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "b", " ", "m"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "p"]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]], "+", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]], "+", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["8", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "b", " ", "m"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "p"]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "+", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]]], " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List["s", "-", FractionBox["v", "2"]]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "-", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]], "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "-", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["8", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "b", " ", "m"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "p"]]]]]]]]], "]"]]]]]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", "p"]]], " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]]]]], ")"]]]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> ∫ </mo> <mrow> <msup> <mi> z </mi> <mi> n </mi> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> p </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mi> m </mi> </msup> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mi> v </mi> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> v </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> m </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> v </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> E </mi> <annotation encoding='Mathematica'> TagBox["E", ExpIntegralE] </annotation> </semantics> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> p </mi> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <semantics> <mrow> <mi> v </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅈ </mi> <mrow> <mo> - </mo> <mi> m </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> v </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <semantics> <mrow> <mi> v </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> m </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> m </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> v </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </munderover> <mrow> <msup> <mi> ⅇ </mi> <mfrac> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <msup> <mi> p </mi> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mi> s </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mi> v </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mi> p </mi> </mfrac> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mi> p </mi> </mfrac> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mi> v </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> v </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mi> s </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mfrac> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mi> v </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mfrac> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mfrac> <mi> v </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mfrac> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <mfrac> <mi> v </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mfrac> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mi> v </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> m </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <mi> v </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <sin /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <ci> m </ci> </apply> <apply> <power /> <apply> <cos /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <ci> v </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> v </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> v </ci> <apply> <times /> <ci> v </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> ExpIntegralE </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> n </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <imaginaryi /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> v </ci> <apply> <times /> <ci> v </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> k </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> b </ci> <imaginaryi /> <ci> k </ci> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> b </ci> <imaginaryi /> <ci> k </ci> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> <ci> b </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> <ci> b </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Binomial </ci> <ci> m </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <sum /> <bvar> <ci> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> v </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> p </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> p </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> v </ci> <ci> s </ci> </apply> <apply> <plus /> <apply> <sum /> <bvar> <ci> q </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> c </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> v </ci> </apply> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <imaginaryi /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> p </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> q </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> v </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> p </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <sum /> <bvar> <ci> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> v </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> <ci> m </ci> <pi /> </apply> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> k </ci> </apply> <apply> <ci> Binomial </ci> <ci> v </ci> <ci> s </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sum /> <bvar> <ci> q </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> b </ci> <imaginaryi /> <ci> k </ci> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> <ci> p </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> k </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> m </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> v </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> b </ci> <imaginaryi /> <ci> k </ci> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> k </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> m </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <imaginaryi /> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sum /> <bvar> <ci> q </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> b </ci> <imaginaryi /> <ci> k </ci> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> <ci> p </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> c </ci> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> v </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> k </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> m </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <imaginaryi /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> b </ci> <imaginaryi /> <ci> k </ci> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> k </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> m </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <imaginaryi /> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <pi /> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> b </ci> <imaginaryi /> <ci> k </ci> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> <ci> p </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sum /> <bvar> <ci> q </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> c </ci> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> v </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> k </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> m </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <imaginaryi /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> k </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> m </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <imaginaryi /> <ci> p </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <pi /> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sum /> <bvar> <ci> q </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> v </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <imaginaryi /> <ci> p </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <ci> p </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> <apply> <in /> <ci> v </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> ℕ </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", SuperscriptBox["z_", "2"]]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "]"]], "m_"], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["c_", " ", "z_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["z", RowBox[List["1", "+", "n"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["ExpIntegralE", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"]]], ",", RowBox[List[RowBox[List["-", "p"]], " ", SuperscriptBox["z", "2"]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ImaginaryI]", RowBox[List["-", "m"]]], " ", SuperscriptBox["z", RowBox[List["1", "+", "n"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "2"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "n"]], "2"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "2"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "2"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "n"]], "2"], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", "p"]], ")"]], " ", SuperscriptBox["z", "2"]]]]], "]"]]]]]], ")"]]]]]]]], "+", RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", "p"]]]], " ", SuperscriptBox["p", RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"], "p"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]], "]"]]]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"], "p"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]], "]"]]]]]]]], ")"]]]]]]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "+", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", "p"]], ")"]]]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", "p"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "b", " ", "k"]], "+", RowBox[List["b", " ", "m"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]], "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "b", " ", "k"]], "+", RowBox[List["b", " ", "m"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["8", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "b", " ", "m"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "p"]]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List["s", "-", FractionBox["v", "2"]]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["8", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "b", " ", "m"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "p"]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]], "+", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]], "+", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["8", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "b", " ", "m"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "p"]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "+", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]]], " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List["s", "-", FractionBox["v", "2"]]], ")"]]]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "-", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]], "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "-", RowBox[List["4", " ", "b", " ", "k", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "m", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "z"]]]], ")"]], "2"]]], RowBox[List[RowBox[List["8", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "b", " ", "m"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "p"]]]]]]]]], "]"]]]]]]]]]], ")"]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", "p"]]], " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]]]]]]]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]], "&&", RowBox[List["v", "\[Element]", "Integers"]], "&&", RowBox[List["v", ">", "0"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|