html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.4022.01

 Input Form

 Integrate[z^n E^(b z^2 + d z + e) Cos[a z^2 + p z + q]^m Cosh[c z^2 + f z + g]^v, z] == (-2^(-1 - m - v)) b^(-1 - n) E^(-(d^2/(4 b)) + e) Binomial[m, m/2] Binomial[v, v/2] (1 - Mod[m, 2]) (1 - Mod[v, 2]) Sum[2^(j - n) (-d)^(-j + n) (d + 2 b z)^(1 + j) (-((d + 2 b z)^2/b))^ ((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + 2 b z)^2/(4 b))], {j, 0, n}] - 2^(-1 - m - v) Binomial[v, v/2] (1 - Mod[v, 2]) Sum[Binomial[m, s] (E^(e - (d + I p (m - 2 s))^2/(4 (b + I a (m - 2 s))) + I q (m - 2 s)) (b + I a (m - 2 s))^(-1 - n) Sum[2^(j - n) (-d - I p (m - 2 s))^ (-j + n) (d + I p (m - 2 s) + 2 (b + I a (m - 2 s)) z)^(1 + j) (-((d + I p (m - 2 s) + 2 (b + I a (m - 2 s)) z)^2/ (b + I a (m - 2 s))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I p (m - 2 s) + 2 (b + I a (m - 2 s)) z)^2/ (4 (b + I a (m - 2 s))))], {j, 0, n}] + E^(e + I q (-m + 2 s) - (d + I p (-m + 2 s))^2/ (4 (b + I a (-m + 2 s)))) (b + I a (-m + 2 s))^(-1 - n) Sum[2^(j - n) (-d - I p (-m + 2 s))^(-j + n) (d + I p (-m + 2 s) + 2 (b + I a (-m + 2 s)) z)^(1 + j) (-((d + I p (-m + 2 s) + 2 (b + I a (-m + 2 s)) z)^2/ (b + I a (-m + 2 s))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I p (-m + 2 s) + 2 (b + I a (-m + 2 s)) z)^ 2/(4 (b + I a (-m + 2 s))))], {j, 0, n}]), {s, 0, Floor[(1/2) (-1 + m)]}] - 2^(-1 - m - v) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[Binomial[v, k] (E^(e - (d + f (2 k - v))^2/(4 (b + c (2 k - v))) + g (2 k - v)) (b + c (2 k - v))^(-1 - n) Sum[2^(j - n) (-d - f (2 k - v))^(-j + n) (d + f (2 k - v) + 2 (b + c (2 k - v)) z)^(1 + j) (-((d + f (2 k - v) + 2 (b + c (2 k - v)) z)^2/(b + c (2 k - v))))^ ((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + f (2 k - v) + 2 (b + c (2 k - v)) z)^2/ (4 (b + c (2 k - v))))], {j, 0, n}] + E^(e + g (-2 k + v) - (d + f (-2 k + v))^2/(4 (b + c (-2 k + v)))) (b + c (-2 k + v))^(-1 - n) Sum[2^(j - n) (-d - f (-2 k + v))^ (-j + n) (d + f (-2 k + v) + 2 (b + c (-2 k + v)) z)^(1 + j) (-((d + f (-2 k + v) + 2 (b + c (-2 k + v)) z)^2/ (b + c (-2 k + v))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + f (-2 k + v) + 2 (b + c (-2 k + v)) z)^2/ (4 (b + c (-2 k + v))))], {j, 0, n}]), {k, 0, Floor[(1/2) (-1 + v)]}] - 2^(-1 - m - v) Sum[Binomial[v, k] Sum[Binomial[m, s] (E^(e + I q (m - 2 s) - (d + I p (m - 2 s) + f (2 k - v))^2/ (4 (b + I a (m - 2 s) + c (2 k - v))) + g (2 k - v)) (b + I a (m - 2 s) + c (2 k - v))^(-1 - n) Sum[2^(j - n) (-d - I p (m - 2 s) - f (2 k - v))^(-j + n) (d + I p (m - 2 s) + f (2 k - v) + 2 (b + I a (m - 2 s) + c (2 k - v)) z)^(1 + j) (-((d + I p (m - 2 s) + f (2 k - v) + 2 (b + I a (m - 2 s) + c (2 k - v)) z)^2/(b + I a (m - 2 s) + c (2 k - v))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I p (m - 2 s) + f (2 k - v) + 2 (b + I a (m - 2 s) + c (2 k - v)) z)^2/(4 (b + I a (m - 2 s) + c (2 k - v))))], {j, 0, n}] + E^(e + I q (-m + 2 s) - (d + I p (-m + 2 s) + f (2 k - v))^2/ (4 (b + I a (-m + 2 s) + c (2 k - v))) + g (2 k - v)) (b + I a (-m + 2 s) + c (2 k - v))^(-1 - n) Sum[2^(j - n) (-d - I p (-m + 2 s) - f (2 k - v))^(-j + n) (d + I p (-m + 2 s) + f (2 k - v) + 2 (b + I a (-m + 2 s) + c (2 k - v)) z)^(1 + j) (-((d + I p (-m + 2 s) + f (2 k - v) + 2 (b + I a (-m + 2 s) + c (2 k - v)) z)^2/(b + I a (-m + 2 s) + c (2 k - v))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I p (-m + 2 s) + f (2 k - v) + 2 (b + I a (-m + 2 s) + c (2 k - v)) z)^2/(4 (b + I a (-m + 2 s) + c (2 k - v))))], {j, 0, n}] + E^(e + I q (m - 2 s) + g (-2 k + v) - (d + I p (m - 2 s) + f (-2 k + v))^2/(4 (b + I a (m - 2 s) + c (-2 k + v)))) (b + I a (m - 2 s) + c (-2 k + v))^(-1 - n) Sum[2^(j - n) (-d - I p (m - 2 s) - f (-2 k + v))^(-j + n) (d + I p (m - 2 s) + f (-2 k + v) + 2 (b + I a (m - 2 s) + c (-2 k + v)) z)^(1 + j) (-((d + I p (m - 2 s) + f (-2 k + v) + 2 (b + I a (m - 2 s) + c (-2 k + v)) z)^2/( b + I a (m - 2 s) + c (-2 k + v))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I p (m - 2 s) + f (-2 k + v) + 2 (b + I a (m - 2 s) + c (-2 k + v)) z)^2/(4 (b + I a (m - 2 s) + c (-2 k + v))))], {j, 0, n}] + E^(e + I q (-m + 2 s) + g (-2 k + v) - (d + I p (-m + 2 s) + f (-2 k + v))^2/(4 (b + I a (-m + 2 s) + c (-2 k + v)))) (b + I a (-m + 2 s) + c (-2 k + v))^(-1 - n) Sum[2^(j - n) (-d - I p (-m + 2 s) - f (-2 k + v))^(-j + n) (d + I p (-m + 2 s) + f (-2 k + v) + 2 (b + I a (-m + 2 s) + c (-2 k + v)) z)^(1 + j) (-((d + I p (-m + 2 s) + f (-2 k + v) + 2 (b + I a (-m + 2 s) + c (-2 k + v)) z)^2/( b + I a (-m + 2 s) + c (-2 k + v))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I p (-m + 2 s) + f (-2 k + v) + 2 (b + I a (-m + 2 s) + c (-2 k + v)) z)^2/(4 (b + I a (-m + 2 s) + c (-2 k + v))))], {j, 0, n}]), {s, 0, Floor[(1/2) (-1 + m)]}], {k, 0, Floor[(1/2) (-1 + v)]}] /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0 && Element[v, Integers] && v > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "n"], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]]], SuperscriptBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["a", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["p", " ", "z"]], "+", "q"]], "]"]], "m"], SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]]]], " ", SuperscriptBox["b", RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["d", "2"], RowBox[List["4", " ", "b"]]]]], "+", "e"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "d"]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], "2"], "b"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "b"]]]]]]], "]"]]]]]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]]]], ")"]]]]]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]]]], ")"]]]]]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "k"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]], ")"]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]], ")"]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]], ")"]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]], ")"]]]]]]]], "]"]]]]]]]]]], ")"]]]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 z n b z 2 + d z + e cos m ( a z 2 + p z + q ) cosh v ( c z 2 + f z + g ) z - 2 - m - v - 1 e - d 2 4 b ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) ( j = 0 n 2 j - n ( - d ) n - j ( d + 2 b z ) j + 1 ( - ( d + 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + 2 b z ) 2 4 b ) ) b - n - 1 - 2 - m - v - 1 ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) s = 0 m - 1 2 ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + p ( 2 s - m ) ) 2 4 ( b + a ( 2 s - m ) ) + e + q ( 2 s - m ) ( j = 0 n 2 j - n ( - d - p ( 2 s - m ) ) n - j ( d + p ( 2 s - m ) + 2 ( b + a ( 2 s - m ) ) z ) j + 1 ( - ( d + p ( 2 s - m ) + 2 ( b + a ( 2 s - m ) ) z ) 2 b + a ( 2 s - m ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + p ( 2 s - m ) + 2 ( b + a ( 2 s - m ) ) z ) 2 4 ( b + a ( 2 s - m ) ) ) ) ( b + a ( 2 s - m ) ) - n - 1 + - ( d + p ( m - 2 s ) ) 2 4 ( b + a ( m - 2 s ) ) + e + q ( m - 2 s ) ( b + a ( m - 2 s ) ) - n - 1 j = 0 n 2 j - n ( - d - p ( m - 2 s ) ) n - j ( d + p ( m - 2 s ) + 2 ( b + a ( m - 2 s ) ) z ) j + 1 ( - ( d + p ( m - 2 s ) + 2 ( b + a ( m - 2 s ) ) z ) 2 b + a ( m - 2 s ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + p ( m - 2 s ) + 2 ( b + a ( m - 2 s ) ) z ) 2 4 ( b + a ( m - 2 s ) ) ) ) - 2 - m - v - 1 ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) k = 0 v - 1 2 ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + f ( 2 k - v ) ) 2 4 ( b + c ( 2 k - v ) ) + e + g ( 2 k - v ) ( j = 0 n 2 j - n ( - d - f ( 2 k - v ) ) n - j ( d + f ( 2 k - v ) + 2 ( b + c ( 2 k - v ) ) z ) j + 1 ( - ( d + f ( 2 k - v ) + 2 ( b + c ( 2 k - v ) ) z ) 2 b + c ( 2 k - v ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + f ( 2 k - v ) + 2 ( b + c ( 2 k - v ) ) z ) 2 4 ( b + c ( 2 k - v ) ) ) ) ( b + c ( 2 k - v ) ) - n - 1 + - ( d + f ( v - 2 k ) ) 2 4 ( b + c ( v - 2 k ) ) + e + g ( v - 2 k ) ( b + c ( v - 2 k ) ) - n - 1 j = 0 n 2 j - n ( - d - f ( v - 2 k ) ) n - j ( d + f ( v - 2 k ) + 2 ( b + c ( v - 2 k ) ) z ) j + 1 ( - ( d + f ( v - 2 k ) + 2 ( b + c ( v - 2 k ) ) z ) 2 b + c ( v - 2 k ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + f ( v - 2 k ) + 2 ( b + c ( v - 2 k ) ) z ) 2 4 ( b + c ( v - 2 k ) ) ) ) - 2 - m - v - 1 k = 0 v - 1 2 ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] s = 0 m - 1 2 ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + p ( 2 s - m ) + f ( 2 k - v ) ) 2 4 ( b + a ( 2 s - m ) + c ( 2 k - v ) ) + e + q ( 2 s - m ) + g ( 2 k - v ) ( j = 0 n 2 j - n ( - d - p ( 2 s - m ) - f ( 2 k - v ) ) n - j ( d + p ( 2 s - m ) + f ( 2 k - v ) + 2 ( b + a ( 2 s - m ) + c ( 2 k - v ) ) z ) j + 1 ( - ( d + p ( 2 s - m ) + f ( 2 k - v ) + 2 ( b + a ( 2 s - m ) + c ( 2 k - v ) ) z ) 2 / ( b + a ( 2 s - m ) + c ( 2 k - v ) ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + p ( 2 s - m ) + f ( 2 k - v ) + 2 ( b + a ( 2 s - m ) + c ( 2 k - v ) ) z ) 2 / ( 4 ( b + a ( 2 s - m ) + c ( 2 k - v ) ) ) ) ) ( b + a ( 2 s - m ) + c ( 2 k - v ) ) - n - 1 + - ( d + p ( m - 2 s ) + f ( 2 k - v ) ) 2 4 ( b + a ( m - 2 s ) + c ( 2 k - v ) ) + e + q ( m - 2 s ) + g ( 2 k - v ) ( b + a ( m - 2 s ) + c ( 2 k - v ) ) - n - 1 j = 0 n 2 j - n ( - d - p ( m - 2 s ) - f ( 2 k - v ) ) n - j ( d + p ( m - 2 s ) + f ( 2 k - v ) + 2 ( b + a ( m - 2 s ) + c ( 2 k - v ) ) z ) j + 1 ( - ( d + p ( m - 2 s ) + f ( 2 k - v ) + 2 ( b + a ( m - 2 s ) + c ( 2 k - v ) ) z ) 2 / ( b + a ( m - 2 s ) + c ( 2 k - v ) ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + p ( m - 2 s ) + f ( 2 k - v ) + 2 ( b + a ( m - 2 s ) + c ( 2 k - v ) ) z ) 2 / ( 4 ( b + a ( m - 2 s ) + c ( 2 k - v ) ) ) ) + - ( d + p ( 2 s - m ) + f ( v - 2 k ) ) 2 4 ( b + a ( 2 s - m ) + c ( v - 2 k ) ) + e + q ( 2 s - m ) + g ( v - 2 k ) ( b + a ( 2 s - m ) + c ( v - 2 k ) ) - n - 1 j = 0 n 2 j - n ( - d - p ( 2 s - m ) - f ( v - 2 k ) ) n - j ( d + p ( 2 s - m ) + f ( v - 2 k ) + 2 ( b + a ( 2 s - m ) + c ( v - 2 k ) ) z ) j + 1 ( - ( d + p ( 2 s - m ) + f ( v - 2 k ) + 2 ( b + a ( 2 s - m ) + c ( v - 2 k ) ) z ) 2 / ( b + a ( 2 s - m ) + c ( v - 2 k ) ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + p ( 2 s - m ) + f ( v - 2 k ) + 2 ( b + a ( 2 s - m ) + c ( v - 2 k ) ) z ) 2 / ( 4 ( b + a ( 2 s - m ) + c ( v - 2 k ) ) ) ) + - ( d + p ( m - 2 s ) + f ( v - 2 k ) ) 2 4 ( b + a ( m - 2 s ) + c ( v - 2 k ) ) + e + q ( m - 2 s ) + g ( v - 2 k ) ( b + a ( m - 2 s ) + c ( v - 2 k ) ) - n - 1 j = 0 n 2 j - n ( - d - p ( m - 2 s ) - f ( v - 2 k ) ) n - j ( d + p ( m - 2 s ) + f ( v - 2 k ) + 2 ( b + a ( m - 2 s ) + c ( v - 2 k ) ) z ) j + 1 ( - ( d + p ( m - 2 s ) + f ( v - 2 k ) + 2 ( b + a ( m - 2 s ) + c ( v - 2 k ) ) z ) 2 / ( b + a ( m - 2 s ) + c ( v - 2 k ) ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + p ( m - 2 s ) + f ( v - 2 k ) + 2 ( b + a ( m - 2 s ) + c ( v - 2 k ) ) z ) 2 / ( 4 ( b + a ( m - 2 s ) + c ( v - 2 k ) ) ) ) ) /; n m + v + Condition z z n b z 2 d z e a z 2 p z q m c z 2 f z g v -1 2 -1 m -1 v -1 e -1 d 2 4 b -1 Binomial m m 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 j 0 n 2 j -1 n -1 d n -1 j d 2 b z j 1 -1 d 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 b z 2 4 b -1 b -1 n -1 -1 2 -1 m -1 v -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 s 0 m -1 2 -1 Binomial m s -1 d p 2 s -1 m 2 4 b a 2 s -1 m -1 e q 2 s -1 m j 0 n 2 j -1 n -1 d -1 p 2 s -1 m n -1 j d p 2 s -1 m 2 b a 2 s -1 m z j 1 -1 d p 2 s -1 m 2 b a 2 s -1 m z 2 b a 2 s -1 m -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d p 2 s -1 m 2 b a 2 s -1 m z 2 4 b a 2 s -1 m -1 b a 2 s -1 m -1 n -1 -1 d p m -1 2 s 2 4 b a m -1 2 s -1 e q m -1 2 s b a m -1 2 s -1 n -1 j 0 n 2 j -1 n -1 d -1 p m -1 2 s n -1 j d p m -1 2 s 2 b a m -1 2 s z j 1 -1 d p m -1 2 s 2 b a m -1 2 s z 2 b a m -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d p m -1 2 s 2 b a m -1 2 s z 2 4 b a m -1 2 s -1 -1 2 -1 m -1 v -1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 k 0 v -1 2 -1 Binomial v k -1 d f 2 k -1 v 2 4 b c 2 k -1 v -1 e g 2 k -1 v j 0 n 2 j -1 n -1 d -1 f 2 k -1 v n -1 j d f 2 k -1 v 2 b c 2 k -1 v z j 1 -1 d f 2 k -1 v 2 b c 2 k -1 v z 2 b c 2 k -1 v -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d f 2 k -1 v 2 b c 2 k -1 v z 2 4 b c 2 k -1 v -1 b c 2 k -1 v -1 n -1 -1 d f v -1 2 k 2 4 b c v -1 2 k -1 e g v -1 2 k b c v -1 2 k -1 n -1 j 0 n 2 j -1 n -1 d -1 f v -1 2 k n -1 j d f v -1 2 k 2 b c v -1 2 k z j 1 -1 d f v -1 2 k 2 b c v -1 2 k z 2 b c v -1 2 k -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d f v -1 2 k 2 b c v -1 2 k z 2 4 b c v -1 2 k -1 -1 2 -1 m -1 v -1 k 0 v -1 2 -1 Binomial v k s 0 m -1 2 -1 Binomial m s -1 d p 2 s -1 m f 2 k -1 v 2 4 b a 2 s -1 m c 2 k -1 v -1 e q 2 s -1 m g 2 k -1 v j 0 n 2 j -1 n -1 d -1 p 2 s -1 m -1 f 2 k -1 v n -1 j d p 2 s -1 m f 2 k -1 v 2 b a 2 s -1 m c 2 k -1 v z j 1 -1 d p 2 s -1 m f 2 k -1 v 2 b a 2 s -1 m c 2 k -1 v z 2 b a 2 s -1 m c 2 k -1 v -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d p 2 s -1 m f 2 k -1 v 2 b a 2 s -1 m c 2 k -1 v z 2 4 b a 2 s -1 m c 2 k -1 v -1 b a 2 s -1 m c 2 k -1 v -1 n -1 -1 d p m -1 2 s f 2 k -1 v 2 4 b a m -1 2 s c 2 k -1 v -1 e q m -1 2 s g 2 k -1 v b a m -1 2 s c 2 k -1 v -1 n -1 j 0 n 2 j -1 n -1 d -1 p m -1 2 s -1 f 2 k -1 v n -1 j d p m -1 2 s f 2 k -1 v 2 b a m -1 2 s c 2 k -1 v z j 1 -1 d p m -1 2 s f 2 k -1 v 2 b a m -1 2 s c 2 k -1 v z 2 b a m -1 2 s c 2 k -1 v -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d p m -1 2 s f 2 k -1 v 2 b a m -1 2 s c 2 k -1 v z 2 4 b a m -1 2 s c 2 k -1 v -1 -1 d p 2 s -1 m f v -1 2 k 2 4 b a 2 s -1 m c v -1 2 k -1 e q 2 s -1 m g v -1 2 k b a 2 s -1 m c v -1 2 k -1 n -1 j 0 n 2 j -1 n -1 d -1 p 2 s -1 m -1 f v -1 2 k n -1 j d p 2 s -1 m f v -1 2 k 2 b a 2 s -1 m c v -1 2 k z j 1 -1 d p 2 s -1 m f v -1 2 k 2 b a 2 s -1 m c v -1 2 k z 2 b a 2 s -1 m c v -1 2 k -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d p 2 s -1 m f v -1 2 k 2 b a 2 s -1 m c v -1 2 k z 2 4 b a 2 s -1 m c v -1 2 k -1 -1 d p m -1 2 s f v -1 2 k 2 4 b a m -1 2 s c v -1 2 k -1 e q m -1 2 s g v -1 2 k b a m -1 2 s c v -1 2 k -1 n -1 j 0 n 2 j -1 n -1 d -1 p m -1 2 s -1 f v -1 2 k n -1 j d p m -1 2 s f v -1 2 k 2 b a m -1 2 s c v -1 2 k z j 1 -1 d p m -1 2 s f v -1 2 k 2 b a m -1 2 s c v -1 2 k z 2 b a m -1 2 s c v -1 2 k -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d p m -1 2 s f v -1 2 k 2 b a m -1 2 s c v -1 2 k z 2 4 b a m -1 2 s c v -1 2 k -1 n m SuperPlus v SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["a_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["p_", " ", "z_"]], "+", "q_"]], "]"]], "m_"], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]]]], " ", SuperscriptBox["b", RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["d", "2"], RowBox[List["4", " ", "b"]]]]], "+", "e"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "d"]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], "2"], "b"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "b"]]]]]]], "]"]]]]]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]]]], ")"]]]]]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]]]], ")"]]]]]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "k"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]]]]]], ")"]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]], "&&", RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]], "&&", RowBox[List["v", "\[Element]", "Integers"]], "&&", RowBox[List["v", ">", "0"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2002-12-18