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/01.20.21.4745.01

 Input Form

 Integrate[Sin[a z^2 + p z + q] Sinh[w z^2 + s z + t] Cosh[c z^2 + f z + g]^v, z] == (-I) 2^(-3 - v) Binomial[v, v/2] (((-E^((-I) q - t - ((-I) p - s)^2/(4 ((-I) a - w)))) ((-I) p - s + 2 ((-I) a - w) z) Gamma[1/2, -(((-I) p - s + 2 ((-I) a - w) z)^2/(4 ((-I) a - w)))])/ (((-I) a - w) Sqrt[-(((-I) p - s + 2 ((-I) a - w) z)^2/ ((-I) a - w))]) + (E^(I q - t - (I p - s)^2/(4 (I a - w))) (I p - s + 2 (I a - w) z) Gamma[1/2, -((I p - s + 2 (I a - w) z)^2/ (4 (I a - w)))])/((I a - w) Sqrt[-((I p - s + 2 (I a - w) z)^2/ (I a - w))]) + (E^((-I) q + t - ((-I) p + s)^2/(4 ((-I) a + w))) ((-I) p + s + 2 ((-I) a + w) z) Gamma[1/2, -(((-I) p + s + 2 ((-I) a + w) z)^2/(4 ((-I) a + w)))])/ (((-I) a + w) Sqrt[-(((-I) p + s + 2 ((-I) a + w) z)^2/ ((-I) a + w))]) - (E^(I q + t - (I p + s)^2/(4 (I a + w))) (I p + s + 2 (I a + w) z) Gamma[1/2, -((I p + s + 2 (I a + w) z)^2/ (4 (I a + w)))])/((I a + w) Sqrt[-((I p + s + 2 (I a + w) z)^2/ (I a + w))])) (1 - Mod[v, 2]) - I 2^(-3 - v) Sum[Binomial[v, h] (((-E^((-I) q - t + g (2 h - v) - ((-I) p - s + f (2 h - v))^2/ (4 ((-I) a + c (2 h - v) - w)))) ((-I) p - s + f (2 h - v) + 2 ((-I) a + c (2 h - v) - w) z) Gamma[1/2, -(((-I) p - s + f (2 h - v) + 2 ((-I) a + c (2 h - v) - w) z)^2/ (4 ((-I) a + c (2 h - v) - w)))])/(((-I) a + c (2 h - v) - w) Sqrt[-(((-I) p - s + f (2 h - v) + 2 ((-I) a + c (2 h - v) - w) z)^2/ ((-I) a + c (2 h - v) - w))]) + (E^(I q - t + g (2 h - v) - (I p - s + f (2 h - v))^2/ (4 (I a + c (2 h - v) - w))) (I p - s + f (2 h - v) + 2 (I a + c (2 h - v) - w) z) Gamma[1/2, -((I p - s + f (2 h - v) + 2 (I a + c (2 h - v) - w) z)^2/ (4 (I a + c (2 h - v) - w)))])/((I a + c (2 h - v) - w) Sqrt[-((I p - s + f (2 h - v) + 2 (I a + c (2 h - v) - w) z)^2/ (I a + c (2 h - v) - w))]) - (E^((-I) q - t + g (-2 h + v) - ((-I) p - s + f (-2 h + v))^2/ (4 ((-I) a + c (-2 h + v) - w))) ((-I) p - s + f (-2 h + v) + 2 ((-I) a + c (-2 h + v) - w) z) Gamma[1/2, -(((-I) p - s + f (-2 h + v) + 2 ((-I) a + c (-2 h + v) - w) z)^2/ (4 ((-I) a + c (-2 h + v) - w)))])/(((-I) a + c (-2 h + v) - w) Sqrt[-(((-I) p - s + f (-2 h + v) + 2 ((-I) a + c (-2 h + v) - w) z)^ 2/((-I) a + c (-2 h + v) - w))]) + (E^(I q - t + g (-2 h + v) - (I p - s + f (-2 h + v))^2/ (4 (I a + c (-2 h + v) - w))) (I p - s + f (-2 h + v) + 2 (I a + c (-2 h + v) - w) z) Gamma[1/2, -((I p - s + f (-2 h + v) + 2 (I a + c (-2 h + v) - w) z)^2/ (4 (I a + c (-2 h + v) - w)))])/((I a + c (-2 h + v) - w) Sqrt[-((I p - s + f (-2 h + v) + 2 (I a + c (-2 h + v) - w) z)^2/ (I a + c (-2 h + v) - w))]) + (E^((-I) q + t + g (2 h - v) - ((-I) p + s + f (2 h - v))^2/ (4 ((-I) a + c (2 h - v) + w))) ((-I) p + s + f (2 h - v) + 2 ((-I) a + c (2 h - v) + w) z) Gamma[1/2, -(((-I) p + s + f (2 h - v) + 2 ((-I) a + c (2 h - v) + w) z)^2/ (4 ((-I) a + c (2 h - v) + w)))])/(((-I) a + c (2 h - v) + w) Sqrt[-(((-I) p + s + f (2 h - v) + 2 ((-I) a + c (2 h - v) + w) z)^2/ ((-I) a + c (2 h - v) + w))]) - (E^(I q + t + g (2 h - v) - (I p + s + f (2 h - v))^2/ (4 (I a + c (2 h - v) + w))) (I p + s + f (2 h - v) + 2 (I a + c (2 h - v) + w) z) Gamma[1/2, -((I p + s + f (2 h - v) + 2 (I a + c (2 h - v) + w) z)^2/ (4 (I a + c (2 h - v) + w)))])/((I a + c (2 h - v) + w) Sqrt[-((I p + s + f (2 h - v) + 2 (I a + c (2 h - v) + w) z)^2/ (I a + c (2 h - v) + w))]) + (E^((-I) q + t + g (-2 h + v) - ((-I) p + s + f (-2 h + v))^2/ (4 ((-I) a + c (-2 h + v) + w))) ((-I) p + s + f (-2 h + v) + 2 ((-I) a + c (-2 h + v) + w) z) Gamma[1/2, -(((-I) p + s + f (-2 h + v) + 2 ((-I) a + c (-2 h + v) + w) z)^2/ (4 ((-I) a + c (-2 h + v) + w)))])/(((-I) a + c (-2 h + v) + w) Sqrt[-(((-I) p + s + f (-2 h + v) + 2 ((-I) a + c (-2 h + v) + w) z)^ 2/((-I) a + c (-2 h + v) + w))]) - (E^(I q + t + g (-2 h + v) - (I p + s + f (-2 h + v))^2/ (4 (I a + c (-2 h + v) + w))) (I p + s + f (-2 h + v) + 2 (I a + c (-2 h + v) + w) z) Gamma[1/2, -((I p + s + f (-2 h + v) + 2 (I a + c (-2 h + v) + w) z)^2/ (4 (I a + c (-2 h + v) + w)))])/((I a + c (-2 h + v) + w) Sqrt[-((I p + s + f (-2 h + v) + 2 (I a + c (-2 h + v) + w) z)^2/ (I a + c (-2 h + v) + w))])), {h, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Sin", "[", RowBox[List[RowBox[List["a", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["p", " ", "z"]], "+", "q"]], "]"]], RowBox[List["Sinh", "[", RowBox[List[RowBox[List["w", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["s", " ", "z"]], "+", "t"]], "]"]], SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]]]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]]]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]]]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]]]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]]]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", "v"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "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", ",", "h"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "-", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]]]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]]]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "-", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", RowBox[List["\[Sqrt]", RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]]]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "+", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]]]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]]]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "+", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", RowBox[List["\[Sqrt]", RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]]]]]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 sin ( a z 2 + p z + q ) sinh ( w z 2 + s z + t ) cosh v ( c z 2 + f z + g ) z - 2 - v - 3 ( - - ( - p - s ) 2 4 ( - a - w ) - q - t ( - p - s + 2 ( - a - w ) z ) Γ ( 1 2 , - ( - p - s + 2 ( - a - w ) z ) 2 4 ( - a - w ) ) ( - a - w ) - ( - p - s + 2 ( - a - w ) z ) 2 - a - w + - ( p - s ) 2 4 ( a - w ) + q - t ( p - s + 2 ( a - w ) z ) Γ ( 1 2 , - ( p - s + 2 ( a - w ) z ) 2 4 ( a - w ) ) ( a - w ) - ( p - s + 2 ( a - w ) z ) 2 a - w + - ( s - p ) 2 4 ( - a + w ) - q + t ( - p + s + 2 ( - a + w ) z ) Γ ( 1 2 , - ( - p + s + 2 ( - a + w ) z ) 2 4 ( - a + w ) ) ( - a + w ) - ( - p + s + 2 ( - a + w ) z ) 2 - a + w - - ( p + s ) 2 4 ( a + w ) + q + t ( p + s + 2 ( a + w ) z ) Γ ( 1 2 , - ( p + s + 2 ( a + w ) z ) 2 4 ( a + w ) ) ( a + w ) - ( p + s + 2 ( a + w ) z ) 2 a + w ) ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["v", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - v mod 2 \$CellContext`v 2 ) - 2 - v - 3 h = 0 v - 1 2 ( v h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["h", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( - ( - ( - p - s + f ( 2 h - v ) ) 2 4 ( - a + c ( 2 h - v ) - w ) - q - t + g ( 2 h - v ) ( - p - s + f ( 2 h - v ) + 2 ( - a + c ( 2 h - v ) - w ) z ) Γ ( 1 2 , - ( - p - s + f ( 2 h - v ) + 2 ( - a + c ( 2 h - v ) - w ) z ) 2 4 ( - a + c ( 2 h - v ) - w ) ) ) / ( ( - a + c ( 2 h - v ) - w ) - ( - p - s + f ( 2 h - v ) + 2 ( - a + c ( 2 h - v ) - w ) z ) 2 - a + c ( 2 h - v ) - w ) + ( - ( p - s + f ( 2 h - v ) ) 2 4 ( a + c ( 2 h - v ) - w ) + q - t + g ( 2 h - v ) ( p - s + f ( 2 h - v ) + 2 ( a + c ( 2 h - v ) - w ) z ) Γ ( 1 2 , - ( p - s + f ( 2 h - v ) + 2 ( a + c ( 2 h - v ) - w ) z ) 2 4 ( a + c ( 2 h - v ) - w ) ) ) / ( ( a + c ( 2 h - v ) - w ) - ( p - s + f ( 2 h - v ) + 2 ( a + c ( 2 h - v ) - w ) z ) 2 a + c ( 2 h - v ) - w ) + ( - ( p - s + f ( v - 2 h ) ) 2 4 ( a + c ( v - 2 h ) - w ) + q - t + g ( v - 2 h ) ( p - s + f ( v - 2 h ) + 2 ( a + c ( v - 2 h ) - w ) z ) Γ ( 1 2 , - ( p - s + f ( v - 2 h ) + 2 ( a + c ( v - 2 h ) - w ) z ) 2 4 ( a + c ( v - 2 h ) - w ) ) ) / ( ( a + c ( v - 2 h ) - w ) - ( p - s + f ( v - 2 h ) + 2 ( a + c ( v - 2 h ) - w ) z ) 2 a + c ( v - 2 h ) - w ) + ( - ( - p + s + f ( 2 h - v ) ) 2 4 ( - a + c ( 2 h - v ) + w ) - q + t + g ( 2 h - v ) ( - p + s + f ( 2 h - v ) + 2 ( - a + c ( 2 h - v ) + w ) z ) Γ ( 1 2 , - ( - p + s + f ( 2 h - v ) + 2 ( - a + c ( 2 h - v ) + w ) z ) 2 4 ( - a + c ( 2 h - v ) + w ) ) ) / ( ( - a + c ( 2 h - v ) + w ) - ( - p + s + f ( 2 h - v ) + 2 ( - a + c ( 2 h - v ) + w ) z ) 2 - a + c ( 2 h - v ) + w ) - ( - ( p + s + f ( 2 h - v ) ) 2 4 ( a + c ( 2 h - v ) + w ) + q + t + g ( 2 h - v ) ( p + s + f ( 2 h - v ) + 2 ( a + c ( 2 h - v ) + w ) z ) Γ ( 1 2 , - ( p + s + f ( 2 h - v ) + 2 ( a + c ( 2 h - v ) + w ) z ) 2 4 ( a + c ( 2 h - v ) + w ) ) ) / ( ( a + c ( 2 h - v ) + w ) - ( p + s + f ( 2 h - v ) + 2 ( a + c ( 2 h - v ) + w ) z ) 2 a + c ( 2 h - v ) + w ) - ( - ( p + s + f ( v - 2 h ) ) 2 4 ( a + c ( v - 2 h ) + w ) + q + t + g ( v - 2 h ) ( p + s + f ( v - 2 h ) + 2 ( a + c ( v - 2 h ) + w ) z ) Γ ( 1 2 , - ( p + s + f ( v - 2 h ) + 2 ( a + c ( v - 2 h ) + w ) z ) 2 4 ( a + c ( v - 2 h ) + w ) ) ) / ( ( a + c ( v - 2 h ) + w ) - ( p + s + f ( v - 2 h ) + 2 ( a + c ( v - 2 h ) + w ) z ) 2 a + c ( v - 2 h ) + w ) - ( - ( - p - s + f ( v - 2 h ) ) 2 4 ( - a + c ( v - 2 h ) - w ) - q - t + g ( v - 2 h ) ( - p - s + f ( v - 2 h ) + 2 ( - a + c ( v - 2 h ) - w ) z ) Γ ( 1 2 , - ( - p - s + f ( v - 2 h ) + 2 ( - a + c ( v - 2 h ) - w ) z ) 2 4 ( - a + c ( v - 2 h ) - w ) ) ) / ( ( - a + c ( v - 2 h ) - w ) - ( - p - s + f ( v - 2 h ) + 2 ( - a + c ( v - 2 h ) - w ) z ) 2 - a + c ( v - 2 h ) - w ) + ( - ( - p + s + f ( v - 2 h ) ) 2 4 ( - a + c ( v - 2 h ) + w ) - q + t + g ( v - 2 h ) ( - p + s + f ( v - 2 h ) + 2 ( - a + c ( v - 2 h ) + w ) z ) Γ ( 1 2 , - ( - p + s + f ( v - 2 h ) + 2 ( - a + c ( v - 2 h ) + w ) z ) 2 4 ( - a + c ( v - 2 h ) + w ) ) ) / ( ( - a + c ( v - 2 h ) + w ) - ( - p + s + f ( v - 2 h ) + 2 ( - a + c ( v - 2 h ) + w ) z ) 2 - a + c ( v - 2 h ) + w ) ) /; v + Condition z a z 2 p z q w z 2 s z t c z 2 f z g v -1 2 -1 v -3 -1 -1 -1 p -1 s 2 4 -1 a -1 w -1 -1 q -1 t -1 p -1 s 2 -1 a -1 w z Gamma 1 2 -1 -1 p -1 s 2 -1 a -1 w z 2 4 -1 a -1 w -1 -1 a -1 w -1 -1 p -1 s 2 -1 a -1 w z 2 -1 a -1 w -1 1 2 -1 -1 p -1 s 2 4 a -1 w -1 q -1 t p -1 s 2 a -1 w z Gamma 1 2 -1 p -1 s 2 a -1 w z 2 4 a -1 w -1 a -1 w -1 p -1 s 2 a -1 w z 2 a -1 w -1 1 2 -1 -1 s -1 p 2 4 -1 a w -1 -1 q t -1 p s 2 -1 a w z Gamma 1 2 -1 -1 p s 2 -1 a w z 2 4 -1 a w -1 -1 a w -1 -1 p s 2 -1 a w z 2 -1 a w -1 1 2 -1 -1 -1 p s 2 4 a w -1 q t p s 2 a w z Gamma 1 2 -1 p s 2 a w z 2 4 a w -1 a w -1 p s 2 a w z 2 a w -1 1 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 -1 2 -1 v -3 h 0 v -1 2 -1 Binomial v h -1 -1 -1 p -1 s f 2 h -1 v 2 4 -1 a c 2 h -1 v -1 w -1 -1 q -1 t g 2 h -1 v -1 p -1 s f 2 h -1 v 2 -1 a c 2 h -1 v -1 w z Gamma 1 2 -1 -1 p -1 s f 2 h -1 v 2 -1 a c 2 h -1 v -1 w z 2 4 -1 a c 2 h -1 v -1 w -1 -1 a c 2 h -1 v -1 w -1 -1 p -1 s f 2 h -1 v 2 -1 a c 2 h -1 v -1 w z 2 -1 a c 2 h -1 v -1 w -1 1 2 -1 -1 p -1 s f 2 h -1 v 2 4 a c 2 h -1 v -1 w -1 q -1 t g 2 h -1 v p -1 s f 2 h -1 v 2 a c 2 h -1 v -1 w z Gamma 1 2 -1 p -1 s f 2 h -1 v 2 a c 2 h -1 v -1 w z 2 4 a c 2 h -1 v -1 w -1 a c 2 h -1 v -1 w -1 p -1 s f 2 h -1 v 2 a c 2 h -1 v -1 w z 2 a c 2 h -1 v -1 w -1 1 2 -1 -1 p -1 s f v -1 2 h 2 4 a c v -1 2 h -1 w -1 q -1 t g v -1 2 h p -1 s f v -1 2 h 2 a c v -1 2 h -1 w z Gamma 1 2 -1 p -1 s f v -1 2 h 2 a c v -1 2 h -1 w z 2 4 a c v -1 2 h -1 w -1 a c v -1 2 h -1 w -1 p -1 s f v -1 2 h 2 a c v -1 2 h -1 w z 2 a c v -1 2 h -1 w -1 1 2 -1 -1 -1 p s f 2 h -1 v 2 4 -1 a c 2 h -1 v w -1 -1 q t g 2 h -1 v -1 p s f 2 h -1 v 2 -1 a c 2 h -1 v w z Gamma 1 2 -1 -1 p s f 2 h -1 v 2 -1 a c 2 h -1 v w z 2 4 -1 a c 2 h -1 v w -1 -1 a c 2 h -1 v w -1 -1 p s f 2 h -1 v 2 -1 a c 2 h -1 v w z 2 -1 a c 2 h -1 v w -1 1 2 -1 -1 -1 p s f 2 h -1 v 2 4 a c 2 h -1 v w -1 q t g 2 h -1 v p s f 2 h -1 v 2 a c 2 h -1 v w z Gamma 1 2 -1 p s f 2 h -1 v 2 a c 2 h -1 v w z 2 4 a c 2 h -1 v w -1 a c 2 h -1 v w -1 p s f 2 h -1 v 2 a c 2 h -1 v w z 2 a c 2 h -1 v w -1 1 2 -1 -1 -1 p s f v -1 2 h 2 4 a c v -1 2 h w -1 q t g v -1 2 h p s f v -1 2 h 2 a c v -1 2 h w z Gamma 1 2 -1 p s f v -1 2 h 2 a c v -1 2 h w z 2 4 a c v -1 2 h w -1 a c v -1 2 h w -1 p s f v -1 2 h 2 a c v -1 2 h w z 2 a c v -1 2 h w -1 1 2 -1 -1 -1 -1 p -1 s f v -1 2 h 2 4 -1 a c v -1 2 h -1 w -1 -1 q -1 t g v -1 2 h -1 p -1 s f v -1 2 h 2 -1 a c v -1 2 h -1 w z Gamma 1 2 -1 -1 p -1 s f v -1 2 h 2 -1 a c v -1 2 h -1 w z 2 4 -1 a c v -1 2 h -1 w -1 -1 a c v -1 2 h -1 w -1 -1 p -1 s f v -1 2 h 2 -1 a c v -1 2 h -1 w z 2 -1 a c v -1 2 h -1 w -1 1 2 -1 -1 -1 p s f v -1 2 h 2 4 -1 a c v -1 2 h w -1 -1 q t g v -1 2 h -1 p s f v -1 2 h 2 -1 a c v -1 2 h w z Gamma 1 2 -1 -1 p s f v -1 2 h 2 -1 a c v -1 2 h w z 2 4 -1 a c v -1 2 h w -1 -1 a c v -1 2 h w -1 -1 p s f v -1 2 h 2 -1 a c v -1 2 h w z 2 -1 a c v -1 2 h w -1 1 2 -1 v SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Sin", "[", RowBox[List[RowBox[List["a_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["p_", " ", "z_"]], "+", "q_"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["w_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["s_", " ", "z_"]], "+", "t_"]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "w"]]]]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "w"]]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "w"]]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "w"]]]]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", "v"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "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", ",", "h"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "-", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]]]]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", "w"]]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "-", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", "w"]]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "+", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "h"]], "-", "v"]], ")"]]]], "+", "w"]]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "q"]], "+", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "h"]], "+", "v"]], ")"]]]], "+", "w"]]]]]]]]]]], ")"]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "&&", RowBox[List["v", ">", "0"]]]]]]]]]]

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

 2002-12-18