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/01.20.21.1425.01

 Input Form

 Integrate[z^n E^(b Sqrt[z] + d z + e) Cos[a Sqrt[z] + p z + q] Cosh[c Sqrt[z] + f z + g], z] == 2^(-3 - 2 n) (E^(e - g - ((-I) a + b - c)^2/(4 (d - f - I p)) - I q) (d - f - I p)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i ((-I) a + b - c)^ (-h - i + 2 n) ((-I) a + b - c + 2 (d - f - I p) Sqrt[z])^(h + i) (-(((-I) a + b - c + 2 (d - f - I p) Sqrt[z])^2/(d - f - I p)))^ ((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] (((-I) a + b - c) ((-I) a + b - c + 2 (d - f - I p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -(((-I) a + b - c + 2 (d - f - I p) Sqrt[ z])^2/(4 (d - f - I p)))] + 2 (d - f - I p) Sqrt[-(((-I) a + b - c + 2 (d - f - I p) Sqrt[z])^2/(d - f - I p))] Gamma[(1/2) (2 + h + i), -(((-I) a + b - c + 2 (d - f - I p) Sqrt[ z])^2/(4 (d - f - I p)))]), {i, 0, n}, {h, 0, i}] + E^(e + g - ((-I) a + b + c)^2/(4 (d + f - I p)) - I q) (d + f - I p)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i ((-I) a + b + c)^ (-h - i + 2 n) ((-I) a + b + c + 2 (d + f - I p) Sqrt[z])^(h + i) (-(((-I) a + b + c + 2 (d + f - I p) Sqrt[z])^2/(d + f - I p)))^ ((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] (((-I) a + b + c) ((-I) a + b + c + 2 (d + f - I p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -(((-I) a + b + c + 2 (d + f - I p) Sqrt[ z])^2/(4 (d + f - I p)))] + 2 (d + f - I p) Sqrt[-(((-I) a + b + c + 2 (d + f - I p) Sqrt[z])^2/(d + f - I p))] Gamma[(1/2) (2 + h + i), -(((-I) a + b + c + 2 (d + f - I p) Sqrt[ z])^2/(4 (d + f - I p)))]), {i, 0, n}, {h, 0, i}] + E^(e - g - (I a + b - c)^2/(4 (d - f + I p)) + I q) (d - f + I p)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (I a + b - c)^(-h - i + 2 n) (I a + b - c + 2 (d - f + I p) Sqrt[z])^ (h + i) (-((I a + b - c + 2 (d - f + I p) Sqrt[z])^2/(d - f + I p)))^ ((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((I a + b - c) (I a + b - c + 2 (d - f + I p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((I a + b - c + 2 (d - f + I p) Sqrt[z])^2/ (4 (d - f + I p)))] + 2 (d - f + I p) Sqrt[-((I a + b - c + 2 (d - f + I p) Sqrt[z])^2/(d - f + I p))] Gamma[(1/2) (2 + h + i), -((I a + b - c + 2 (d - f + I p) Sqrt[z])^2/ (4 (d - f + I p)))]), {i, 0, n}, {h, 0, i}] + E^(e + g - (I a + b + c)^2/(4 (d + f + I p)) + I q) (d + f + I p)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (I a + b + c)^(-h - i + 2 n) (I a + b + c + 2 (d + f + I p) Sqrt[z])^ (h + i) (-((I a + b + c + 2 (d + f + I p) Sqrt[z])^2/(d + f + I p)))^ ((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((I a + b + c) (I a + b + c + 2 (d + f + I p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((I a + b + c + 2 (d + f + I p) Sqrt[z])^2/ (4 (d + f + I p)))] + 2 (d + f + I p) Sqrt[-((I a + b + c + 2 (d + f + I p) Sqrt[z])^2/(d + f + I p))] Gamma[(1/2) (2 + h + i), -((I a + b + c + 2 (d + f + I p) Sqrt[z])^2/ (4 (d + f + I p)))]), {i, 0, n}, {h, 0, i}]) /; 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[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]]], RowBox[List["Cos", "[", RowBox[List[RowBox[List["a", " ", SqrtBox["z"]]], "+", RowBox[List["p", " ", "z"]], "+", "q"]], "]"]], RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "-", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "-", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 z n z b + d z + e cos ( z a + p z + q ) cosh ( z c + f z + g ) z 2 - 2 n - 3 ( - ( b - c + a ) 2 4 ( d - f + p ) + e - g + q ( d - f + p ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b - c + a ) - h - i + 2 n ( b - c + a + 2 ( d - f + p ) z ) h + i ( - ( b - c + a + 2 ( d - f + p ) z ) 2 d - f + p ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( b - c + a ) ( b - c + a + 2 ( d - f + p ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( b - c + a + 2 ( d - f + p ) z ) 2 4 ( d - f + p ) ) + 2 - ( b - c + a + 2 ( d - f + p ) z ) 2 d - f + p ( d - f + p ) Γ ( 1 2 ( h + i + 2 ) , - ( b - c + a + 2 ( d - f + p ) z ) 2 4 ( d - f + p ) ) ) + - ( b + c + a ) 2 4 ( d + f + p ) + e + g + q ( d + f + p ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b + c + a ) - h - i + 2 n ( b + c + a + 2 ( d + f + p ) z ) h + i ( - ( b + c + a + 2 ( d + f + p ) z ) 2 d + f + p ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( b + c + a ) ( b + c + a + 2 ( d + f + p ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( b + c + a + 2 ( d + f + p ) z ) 2 4 ( d + f + p ) ) + 2 - ( b + c + a + 2 ( d + f + p ) z ) 2 d + f + p ( d + f + p ) Γ ( 1 2 ( h + i + 2 ) , - ( b + c + a + 2 ( d + f + p ) z ) 2 4 ( d + f + p ) ) ) + - ( b - c - a ) 2 4 ( d - f - p ) + e - g - q ( d - f - p ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b - c - a ) - h - i + 2 n ( b - c - a + 2 ( d - f - p ) z ) h + i ( - ( b - c - a + 2 ( d - f - p ) z ) 2 d - f - p ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( b - c - a ) ( b - c - a + 2 ( d - f - p ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( b - c - a + 2 ( d - f - p ) z ) 2 4 ( d - f - p ) ) + 2 - ( b - c - a + 2 ( d - f - p ) z ) 2 d - f - p ( d - f - p ) Γ ( 1 2 ( h + i + 2 ) , - ( b - c - a + 2 ( d - f - p ) z ) 2 4 ( d - f - p ) ) ) + - ( b + c - a ) 2 4 ( d + f - p ) + e + g - q ( d + f - p ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b + c - a ) - h - i + 2 n ( b + c - a + 2 ( d + f - p ) z ) h + i ( - ( b + c - a + 2 ( d + f - p ) z ) 2 d + f - p ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( b + c - a ) ( b + c - a + 2 ( d + f - p ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( b + c - a + 2 ( d + f - p ) z ) 2 4 ( d + f - p ) ) + 2 - ( b + c - a + 2 ( d + f - p ) z ) 2 d + f - p ( d + f - p ) Γ ( 1 2 ( h + i + 2 ) , - ( b + c - a + 2 ( d + f - p ) z ) 2 4 ( d + f - p ) ) ) ) /; n Condition z z n z 1 2 b d z e z 1 2 a p z q z 1 2 c f z g 2 -2 n -3 -1 b -1 c a 2 4 d -1 f p -1 e -1 g q d -1 f p -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b -1 c a -1 h -1 i 2 n b -1 c a 2 d -1 f p z 1 2 h i -1 b -1 c a 2 d -1 f p z 1 2 2 d -1 f p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b -1 c a b -1 c a 2 d -1 f p z 1 2 Gamma 1 2 h i 1 -1 b -1 c a 2 d -1 f p z 1 2 2 4 d -1 f p -1 2 -1 b -1 c a 2 d -1 f p z 1 2 2 d -1 f p -1 1 2 d -1 f p Gamma 1 2 h i 2 -1 b -1 c a 2 d -1 f p z 1 2 2 4 d -1 f p -1 -1 b c a 2 4 d f p -1 e g q d f p -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b c a -1 h -1 i 2 n b c a 2 d f p z 1 2 h i -1 b c a 2 d f p z 1 2 2 d f p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b c a b c a 2 d f p z 1 2 Gamma 1 2 h i 1 -1 b c a 2 d f p z 1 2 2 4 d f p -1 2 -1 b c a 2 d f p z 1 2 2 d f p -1 1 2 d f p Gamma 1 2 h i 2 -1 b c a 2 d f p z 1 2 2 4 d f p -1 -1 b -1 c -1 a 2 4 d -1 f -1 p -1 e -1 g -1 q d -1 f -1 p -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b -1 c -1 a -1 h -1 i 2 n b -1 c -1 a 2 d -1 f -1 p z 1 2 h i -1 b -1 c -1 a 2 d -1 f -1 p z 1 2 2 d -1 f -1 p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b -1 c -1 a b -1 c -1 a 2 d -1 f -1 p z 1 2 Gamma 1 2 h i 1 -1 b -1 c -1 a 2 d -1 f -1 p z 1 2 2 4 d -1 f -1 p -1 2 -1 b -1 c -1 a 2 d -1 f -1 p z 1 2 2 d -1 f -1 p -1 1 2 d -1 f -1 p Gamma 1 2 h i 2 -1 b -1 c -1 a 2 d -1 f -1 p z 1 2 2 4 d -1 f -1 p -1 -1 b c -1 a 2 4 d f -1 p -1 e g -1 q d f -1 p -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b c -1 a -1 h -1 i 2 n b c -1 a 2 d f -1 p z 1 2 h i -1 b c -1 a 2 d f -1 p z 1 2 2 d f -1 p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b c -1 a b c -1 a 2 d f -1 p z 1 2 Gamma 1 2 h i 1 -1 b c -1 a 2 d f -1 p z 1 2 2 4 d f -1 p -1 2 -1 b c -1 a 2 d f -1 p z 1 2 2 d f -1 p -1 1 2 d f -1 p Gamma 1 2 h i 2 -1 b c -1 a 2 d f -1 p z 1 2 2 4 d f -1 p -1 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[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]]], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["a_", " ", SqrtBox["z_"]]], "+", RowBox[List["p_", " ", "z_"]], "+", "q_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "-", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "-", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2002-12-18