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/01.20.21.3645.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["n", "-", "1"]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]], "-", "v"]]], " ", SuperscriptBox["d", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["b", "2"]]], RowBox[List["4", " ", "d"]]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "j"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "j"]]], " ", SuperscriptBox["4", "j"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "j", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"]]], "d"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["j", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"]]], RowBox[List["4", " ", "d"]]]]]]], "]"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"]]], "d"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"]]], RowBox[List["4", " ", "d"]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["b", "2"]]], RowBox[List["4", " ", "d"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "e"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "j"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "j"]]], " ", SuperscriptBox["4", "j"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "j", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"]]], "d"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["j", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "j"]], ")"]]]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"]]], RowBox[List["4", " ", "d"]]]]], "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"]]], "d"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "j"]], ")"]]]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"]]], RowBox[List["4", " ", "d"]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]], "-", "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["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "e"]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", 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[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "j"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "j"]]], " ", SuperscriptBox["4", "j"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "j", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["j", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "e"]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", 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[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "j"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "j"]]], " ", SuperscriptBox["4", "j"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "j", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["j", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "e"]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "j"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "j"]]], " ", SuperscriptBox["4", "j"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "j", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["j", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "e"]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "j"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "j"]]], " ", SuperscriptBox["4", "j"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "j", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["j", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", RowBox[List["f", " ", 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["v", "\[Element]", "Integers"]], "&&", RowBox[List["v", ">", "0"]]]]]]]]]]

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

 2002-12-18