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/01.20.21.1382.01

 Input Form

 Integrate[z^n E^(p z^2) Sin[b z^2]^m Cosh[c z], z] == ((1/Sqrt[p]) 2^(-2 - m) (Binomial[m, m/2] (-1 + Mod[m, 2]) (Sum[2^(-n + q) c^(n - q) p^(-(1/2) - n) (-((c - 2 p z)^2/p))^ ((1/2) (-1 - q)) (-c + 2 p z)^(1 + q) Binomial[n, q] Gamma[(1 + q)/2, -((c - 2 p z)^2/(4 p))], {q, 0, n}] + Sum[2^(-n + q) (-c)^(n - q) p^(-(1/2) - n) (c + 2 p z)^(1 + q) (-((c + 2 p z)^2/p))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((c + 2 p z)^2/(4 p))], {q, 0, n}]) + (-I)^m E^(c^2/(4 p)) Sqrt[p] Sum[(-1)^k Binomial[m, k] (-(E^(c^2/(8 I b k - 4 I b m - 4 p)) Sum[2^(-n + q) c^(n - q) (-2 I b k + I b m + p)^(-(1/2) - n) (-((c + 4 I b k z - 2 I b m z - 2 p z)^2/(-2 I b k + I b m + p)))^((1/2) (-1 - q)) (-c + 2 (-2 I b k + I b m + p) z)^( 1 + q) Binomial[n, q] Gamma[(1 + q)/2, -((c + 4 I b k z - 2 I b m z - 2 p z)^2/(4 (-2 I b k + I b m + p)))], {q, 0, n}])/Sqrt[-2 I b k + I b m + p] - (E^(c^2/(-8 I b k + 4 I b m - 4 p) + I m Pi) Sum[2^(-n + q) c^(n - q) (2 I b k - I b m + p)^(-(1/2) - n) (-((c - 2 (2 I b k - I b m + p) z)^2/(2 I b k - I b m + p)))^ ((1/2) (-1 - q)) (-c + 2 (2 I b k - I b m + p) z)^(1 + q) Binomial[n, q] Gamma[(1 + q)/2, -((c - 2 (2 I b k - I b m + p) z)^2/(4 (2 I b k - I b m + p)))], {q, 0, n}])/ Sqrt[2 I b k - I b m + p] - (E^(c^2/(-8 I b k + 4 I b m - 4 p) + I m Pi) Sum[2^(-n + q) (-c)^(n - q) (2 I b k - I b m + p)^(-(1/2) - n) (c + 2 (2 I b k - I b m + p) z)^(1 + q) (-((c + 2 (2 I b k - I b m + p) z)^2/(2 I b k - I b m + p)))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((c + 2 (2 I b k - I b m + p) z)^2/(4 (2 I b k - I b m + p)))], {q, 0, n}])/Sqrt[2 I b k - I b m + p] - (E^(c^2/(8 I b k - 4 I b m - 4 p)) Sum[2^(-n + q) (-c)^(n - q) (-2 I b k + I b m + p)^(-(1/2) - n) (c + 2 (-2 I b k + I b m + p) z)^(1 + q) (-((c + 2 (-2 I b k + I b m + p) z)^2/ (-2 I b k + I b m + p)))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((c + 2 (-2 I b k + I b m + p) z)^2/ (4 (-2 I b k + I b m + p)))], {q, 0, n}])/ Sqrt[-2 I b k + I b m + p]), {k, 0, Floor[(1/2) (-1 + m)]}]))/ E^(c^2/(4 p)) /; Element[m, Integers] && m > 0 && Element[n, Integers] && n >= 0

 Standard Form

 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"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox["p"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["(", RowBox[List[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["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox["c", RowBox[List["n", "-", "q"]]], " ", SuperscriptBox["p", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], "2"], "p"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", 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"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "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["-", "c"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox["p", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], "2"], "p"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[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[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]]]], "]"]]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "\[ImaginaryI]"]], ")"]], "m"], SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "p"]]]], " ", SqrtBox["p"], " ", 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[RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox["c", 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["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "m", " ", "z"]], "-", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", 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"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "m", " ", "z"]], "-", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]]]], "]"]]]]]]]], ")"]]]], "/", RowBox[List["(", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["4", " ", "p"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox["c", RowBox[List["n", "-", "q"]]], " ", 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["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", 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[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]]]], "]"]]]]]]]], ")"]], "/", RowBox[List["(", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["4", " ", "p"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "c"]], ")"]], RowBox[List["n", "-", "q"]]], " ", 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["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[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[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]]]], "]"]]]]]]]], ")"]], "/", RowBox[List["(", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]], "-", 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["-", "c"]], ")"]], 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["c", "+", 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"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[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[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]]]], "]"]]]]]]]], ")"]], "/", RowBox[List["(", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], ")"]]]]]], ")"]]]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 z n p z 2 sin m ( b z 2 ) cosh ( c z ) z 1 p ( 2 - m - 2 - c 2 4 p ( c 2 4 p p ( k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( c 2 8 b k - 4 b m - 4 p q = 0 n 2 q - n c n - q ( - 2 b k + b m + p ) - n - 1 2 ( - ( c + 4 b k z - 2 b m z - 2 p z ) 2 - 2 b k + b m + p ) 1 2 ( - q - 1 ) ( 2 ( - 2 b k + b m + p ) z - c ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( c + 4 b k z - 2 b m z - 2 p z ) 2 4 ( - 2 b k + b m + p ) ) ) / ( - 2 b k + b m + p ) - ( c 2 8 b k - 4 b m - 4 p q = 0 n 2 q - n ( - c ) n - q ( - 2 b k + b m + p ) - n - 1 2 ( c + 2 ( - 2 b k + b m + p ) z ) q + 1 ( - ( c + 2 ( - 2 b k + b m + p ) z ) 2 - 2 b k + b m + p ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( c + 2 ( - 2 b k + b m + p ) z ) 2 4 ( - 2 b k + b m + p ) ) ) / ( - 2 b k + b m + p ) - 1 2 b k - b m + p ( c 2 - 8 b k + 4 b m - 4 p + m π q = 0 n 2 q - n ( - c ) n - q ( 2 b k - b m + p ) - n - 1 2 ( c + 2 ( 2 b k - b m + p ) z ) q + 1 ( - ( c + 2 ( 2 b k - b m + p ) z ) 2 2 b k - b m + p ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( c + 2 ( 2 b k - b m + p ) z ) 2 4 ( 2 b k - b m + p ) ) ) - 1 2 b k - b m + p ( c 2 - 8 b k + 4 b m - 4 p + m π q = 0 n 2 q - n c n - q ( 2 b k - b m + p ) - n - 1 2 ( - ( c - 2 ( 2 b k - b m + p ) z ) 2 2 b k - b m + p ) 1 2 ( - q - 1 ) ( 2 ( 2 b k - b m + p ) z - c ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( c - 2 ( 2 b k - b m + p ) z ) 2 4 ( 2 b k - b m + p ) ) ) ) ) ( - ) m + ( 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]]]]] ( m mod 2 \$CellContext`m 2 - 1 ) ( q = 0 n 2 q - n ( - c ) n - q p - n - 1 2 ( c + 2 p z ) q + 1 ( - ( c + 2 p z ) 2 p ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( c + 2 p z ) 2 4 p ) + q = 0 n 2 q - n c n - q p - n - 1 2 ( - ( c - 2 p z ) 2 p ) 1 2 ( - q - 1 ) ( 2 p z - c ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( c - 2 p z ) 2 4 p ) ) ) ) /; m TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] m > 0 n Condition z z n p z 2 b z 2 m c z 1 p 1 2 -1 2 -1 m -2 -1 c 2 4 p -1 c 2 4 p -1 p 1 2 k 0 m -1 2 -1 -1 k Binomial m k -1 c 2 8 b k -1 4 b m -1 4 p -1 q 0 n 2 q -1 n c n -1 q -2 b k b m p -1 n -1 1 2 -1 c 4 b k z -1 2 b m z -1 2 p z 2 -2 b k b m p -1 1 2 -1 q -1 2 -2 b k b m p z -1 c q 1 Binomial n q Gamma q 1 2 -1 -1 c 4 b k z -1 2 b m z -1 2 p z 2 4 -2 b k b m p -1 -2 b k b m p 1 2 -1 -1 c 2 8 b k -1 4 b m -1 4 p -1 q 0 n 2 q -1 n -1 c n -1 q -2 b k b m p -1 n -1 1 2 c 2 -2 b k b m p z q 1 -1 c 2 -2 b k b m p z 2 -2 b k b m p -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 c 2 -2 b k b m p z 2 4 -2 b k b m p -1 -2 b k b m p 1 2 -1 -1 1 2 b k -1 b m p 1 2 -1 c 2 -8 b k 4 b m -1 4 p -1 m q 0 n 2 q -1 n -1 c n -1 q 2 b k -1 b m p -1 n -1 1 2 c 2 2 b k -1 b m p z q 1 -1 c 2 2 b k -1 b m p z 2 2 b k -1 b m p -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 c 2 2 b k -1 b m p z 2 4 2 b k -1 b m p -1 -1 1 2 b k -1 b m p 1 2 -1 c 2 -8 b k 4 b m -1 4 p -1 m q 0 n 2 q -1 n c n -1 q 2 b k -1 b m p -1 n -1 1 2 -1 c -1 2 2 b k -1 b m p z 2 2 b k -1 b m p -1 1 2 -1 q -1 2 2 b k -1 b m p z -1 c q 1 Binomial n q Gamma q 1 2 -1 -1 c -1 2 2 b k -1 b m p z 2 4 2 b k -1 b m p -1 -1 m Binomial m m 2 -1 \$CellContext`m 2 -1 q 0 n 2 q -1 n -1 c n -1 q p -1 n -1 1 2 c 2 p z q 1 -1 c 2 p z 2 p -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 c 2 p z 2 4 p -1 q 0 n 2 q -1 n c n -1 q p -1 n -1 1 2 -1 c -1 2 p z 2 p -1 1 2 -1 q -1 2 p z -1 c q 1 Binomial n q Gamma q 1 2 -1 -1 c -1 2 p z 2 4 p -1 m m 0 n [/itex]

 Rule Form

 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_"], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["(", RowBox[List[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["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox["c", RowBox[List["n", "-", "q"]]], " ", SuperscriptBox["p", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], "2"], "p"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", 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"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "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["-", "c"]], ")"]], RowBox[List["n", "-", "q"]]], " ", SuperscriptBox["p", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], "2"], "p"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[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[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]]]], "]"]]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "\[ImaginaryI]"]], ")"]], "m"], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "p"]]]], " ", SqrtBox["p"], " ", 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["-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox["c", 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["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "m", " ", "z"]], "-", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", 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"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "k", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "m", " ", "z"]], "-", RowBox[List["2", " ", "p", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", 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"]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["4", " ", "p"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox["c", RowBox[List["n", "-", "q"]]], " ", 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["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", 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[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "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["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["4", " ", "p"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["q", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "c"]], ")"]], RowBox[List["n", "-", "q"]]], " ", 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["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[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[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "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["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List["8", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", "b", " ", "m"]], "-", 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["-", "c"]], ")"]], 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["c", "+", 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"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[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[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", 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"]]]]]], ")"]]]]]]]]]], ")"]]]], SqrtBox["p"]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2002-12-18