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; }

 Cos

 http://functions.wolfram.com/01.07.21.2737.01

 Input Form

 Integrate[z^n E^(b z^2 + d z + e) Sin[a z^2 + p z + q] Cos[c z^2 + f z + g]^v, z] == 2^(-2 - v) ((-Binomial[v, v/2]) (1 - Mod[v, 2]) (I ((-I) a + b)^(-1 - n) E^(e - (d - I p)^2/(4 ((-I) a + b)) - I q) Sum[2^(j - n) (-d + I p)^(-j + n) ((I (I d + p + 2 a z + 2 I b z)^2)/ (a + I b))^((1/2) (-1 - j)) (d - I (p + 2 a z + 2 I b z))^(1 + j) Binomial[n, j] Gamma[(1 + j)/2, (I (I d + p + 2 a z + 2 I b z)^2)/ (4 (a + I b))], {j, 0, n}] - I (I a + b)^(-1 - n) E^(e - (d + I p)^2/(4 (I a + b)) + I q) Sum[2^(j - n) (-d - I p)^(-j + n) (d + I p + 2 I a z + 2 b z)^(1 + j) (-((d + I p + 2 I a z + 2 b z)^2/(I a + b)))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I p + 2 I a z + 2 b z)^2/ (4 (I a + b)))], {j, 0, n}]) - Sum[I E^(e - I (q + 2 g s - g v)) Binomial[v, s] ((I E^((1/4) I (8 q + 8 g (2 s - v) + (d + I (p + 2 f s - f v))^2/ (a - I b + 2 c s - c v))) Sum[2^(j - n) (-d - I (p + 2 f s - f v))^(-j + n) (-((I ((-I) d + p + 2 f s - f v + 2 a z - 2 I b z + 4 c s z - 2 c v z)^2)/(a - I b + 2 c s - c v)))^((1/2) (-1 - j)) (d + I (p + f (2 s - v) + 2 (a - I b + 2 c s - c v) z))^(1 + j) Binomial[n, j] Gamma[(1 + j)/2, -((I ((-I) d + p + 2 f s - f v + 2 a z - 2 I b z + 4 c s z - 2 c v z)^2)/(4 (a - I b + 2 c s - c v)))], {j, 0, n}])/(I a + b + 2 I c s - I c v)^n/ (a - I b + 2 c s - c v) + (I E^((I (I d + p + 2 f s - f v)^2)/(4 (a + I b + 2 c s - c v))) Sum[2^(j - n) (-d + I (p + 2 f s - f v))^(-j + n) ((I (I d + p + 2 f s - f v + 2 a z + 2 I b z + 4 c s z - 2 c v z)^ 2)/(a + I b + 2 c s - c v))^((1/2) (-1 - j)) (d - I (p + f (2 s - v) + 2 (a + I b + 2 c s - c v) z))^(1 + j) Binomial[n, j] Gamma[(1 + j)/2, (I (I d + p + 2 f s - f v + 2 a z + 2 I b z + 4 c s z - 2 c v z)^2)/(4 (a + I b + 2 c s - c v))], {j, 0, n}])/((-I) a + b + I c (-2 s + v))^n/ (a + I b + 2 c s - c v) - E^((1/4) I (8 q + (d + I (p - 2 f s + f v))^2/(a - I b - 2 c s + c v))) (I a + b + I c (-2 s + v))^(-1 - n) Sum[2^(j - n) (-d - I (p - 2 f s + f v))^(-j + n) (-((I ((-I) d + p - 2 f s + f v + 2 a z - 2 I b z - 4 c s z + 2 c v z)^2)/(a - I b - 2 c s + c v)))^((1/2) (-1 - j)) (d + I (p + f (-2 s + v) + 2 (a - I b - 2 c s + c v) z))^(1 + j) Binomial[n, j] Gamma[(1 + j)/2, -((I ((-I) d + p - 2 f s + f v + 2 a z - 2 I b z - 4 c s z + 2 c v z)^2)/(4 (a - I b - 2 c s + c v)))], {j, 0, n}] + E^((1/4) I (8 g (2 s - v) + (I d + p - 2 f s + f v)^2/ (a + I b - 2 c s + c v))) ((-I) (a + I b - 2 c s + c v))^(-1 - n) Sum[(-I) 2^(j - n) (-d + I (p - 2 f s + f v))^(-j + n) (I d + p - 2 f s + f v + 2 a z + 2 I b z - 4 c s z + 2 c v z) ((I (I d + p - 2 f s + f v + 2 a z + 2 I b z - 4 c s z + 2 c v z)^ 2)/(a + I b - 2 c s + c v))^((1/2) (-1 - j)) (d - I (p + f (-2 s + v) + 2 (a + I b - 2 c s + c v) z))^j Binomial[n, j] Gamma[(1 + j)/2, (I (I d + p - 2 f s + f v + 2 a z + 2 I b z - 4 c s z + 2 c v z)^ 2)/(4 (a + I b - 2 c s + c v))], {j, 0, n}]), {s, 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"], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]]], RowBox[List["Sin", "[", RowBox[List[RowBox[List["a", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["p", " ", "z"]], "+", "q"]], "]"]], SuperscriptBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["c", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "v"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", 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["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]]]]], "-", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]]]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]]]]], "]"]]]]]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]]]]]]]]], "]"]]]]]]]]]], ")"]]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["q", "+", RowBox[List["2", " ", "g", " ", "s"]], "-", RowBox[List["g", " ", "v"]]]], ")"]]]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", "q"]], "+", RowBox[List["8", " ", "g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], "2"], RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]]]]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "s"]], "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "v"]]]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "+", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], ")"]], "/", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "+", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], ")"]], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]]]], ")"]]]]]]]], "]"]]]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "+", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], ")"]], "/", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "+", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], ")"]], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]]]], ")"]]]]]], "]"]]]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", "q"]], "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], "2"], RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]]]]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], ")"]], "/", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], ")"]], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]]]], ")"]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", "g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]]]], ")"]], "2"], RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]]]]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], ")"]], "/", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]], "j"], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], ")"]], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "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 b z 2 + d z + e sin ( a z 2 + p z + q ) cos v ( c z 2 + f z + g ) z 2 - 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 ) ( ( b - a ) - n - 1 - ( d - p ) 2 4 ( b - a ) + e - q j = 0 n 2 j - n ( p - d ) n - j ( ( d + p + 2 a z + 2 b z ) 2 a + b ) 1 2 ( - j - 1 ) ( d - ( p + 2 a z + 2 b z ) ) j + 1 ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( d + p + 2 a z + 2 b z ) 2 4 ( a + b ) ) - ( b + a ) - n - 1 - ( d + p ) 2 4 ( b + a ) + e + q j = 0 n 2 j - n ( - d - p ) n - j ( d + p + 2 b z + 2 a z ) j + 1 ( - ( d + p + 2 b z + 2 a z ) 2 b + a ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + p + 2 b z + 2 a z ) 2 4 ( b + a ) ) ) - s = 0 v - 1 2 e - ( q + 2 g s - g v ) ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 4 ( ( d + p - 2 f s + f v ) 2 a + b - 2 c s + c v + 8 g ( 2 s - v ) ) ( j = 0 n - 2 j - n ( ( p - 2 f s + f v ) - d ) n - j ( d + p - 2 f s + f v + 2 a z + 2 b z - 4 c s z + 2 c v z ) ( ( d + p - 2 f s + f v + 2 a z + 2 b z - 4 c s z + 2 c v z ) 2 a + b - 2 c s + c v ) 1 2 ( - j - 1 ) ( d - ( p + f ( v - 2 s ) + 2 ( a + b - 2 c s + c v ) z ) ) j ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( d + p - 2 f s + f v + 2 a z + 2 b z - 4 c s z + 2 c v z ) 2 4 ( a + b - 2 c s + c v ) ) ) ( - ( a + b - 2 c s + c v ) ) - n - 1 - 1 4 ( ( d + ( p - 2 f s + f v ) ) 2 a - b - 2 c s + c v + 8 q ) ( b + a + c ( v - 2 s ) ) - n - 1 j = 0 n 2 j - n ( - d - ( p - 2 f s + f v ) ) n - j ( - ( - d + p - 2 f s + f v + 2 a z - 2 b z - 4 c s z + 2 c v z ) 2 a - b - 2 c s + c v ) 1 2 ( - j - 1 ) ( d + ( p + f ( v - 2 s ) + 2 ( a - b - 2 c s + c v ) z ) ) j + 1 ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( - d + p - 2 f s + f v + 2 a z - 2 b z - 4 c s z + 2 c v z ) 2 4 ( a - b - 2 c s + c v ) ) + 1 a + b + 2 c s - c v ( ( d + p + 2 f s - f v ) 2 4 ( a + b + 2 c s - c v ) ( b - a + c ( v - 2 s ) ) - n j = 0 n 2 j - n ( ( p + 2 f s - f v ) - d ) n - j ( ( d + p + 2 f s - f v + 2 a z + 2 b z + 4 c s z - 2 c v z ) 2 a + b + 2 c s - c v ) 1 2 ( - j - 1 ) ( d - ( p + f ( 2 s - v ) + 2 ( a + b + 2 c s - c v ) z ) ) j + 1 ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( d + p + 2 f s - f v + 2 a z + 2 b z + 4 c s z - 2 c v z ) 2 4 ( a + b + 2 c s - c v ) ) ) + 1 a - b + 2 c s - c v ( 1 4 ( ( d + ( p + 2 f s - f v ) ) 2 a - b + 2 c s - c v + 8 q + 8 g ( 2 s - v ) ) ( b + a + 2 c s - c v ) - n j = 0 n 2 j - n ( - d - ( p + 2 f s - f v ) ) n - j ( - ( - d + p + 2 f s - f v + 2 a z - 2 b z + 4 c s z - 2 c v z ) 2 a - b + 2 c s - c v ) 1 2 ( - j - 1 ) ( d + ( p + f ( 2 s - v ) + 2 ( a - b + 2 c s - c v ) z ) ) j + 1 ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( - d + p + 2 f s - f v + 2 a z - 2 b z + 4 c s z - 2 c v z ) 2 4 ( a - b + 2 c s - c v ) ) ) ) ) /; n v + Condition z z n b z 2 d z e a z 2 p z q c z 2 f z g v 2 -1 v -2 -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 b -1 a -1 n -1 -1 d -1 p 2 4 b -1 a -1 e -1 q j 0 n 2 j -1 n p -1 d n -1 j d p 2 a z 2 b z 2 a b -1 1 2 -1 j -1 d -1 p 2 a z 2 b z j 1 Binomial n j Gamma j 1 2 -1 d p 2 a z 2 b z 2 4 a b -1 -1 b a -1 n -1 -1 d p 2 4 b a -1 e q j 0 n 2 j -1 n -1 d -1 p n -1 j d p 2 b z 2 a z j 1 -1 d p 2 b z 2 a z 2 b a -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d p 2 b z 2 a z 2 4 b a -1 -1 s 0 v -1 2 -1 e -1 q 2 g s -1 g v Binomial v s 1 4 d p -1 2 f s f v 2 a b -1 2 c s c v -1 8 g 2 s -1 v j 0 n -1 2 j -1 n p -1 2 f s f v -1 d n -1 j d p -1 2 f s f v 2 a z 2 b z -1 4 c s z 2 c v z d p -1 2 f s f v 2 a z 2 b z -1 4 c s z 2 c v z 2 a b -1 2 c s c v -1 1 2 -1 j -1 d -1 p f v -1 2 s 2 a b -1 2 c s c v z j Binomial n j Gamma j 1 2 -1 d p -1 2 f s f v 2 a z 2 b z -1 4 c s z 2 c v z 2 4 a b -1 2 c s c v -1 -1 a b -1 2 c s c v -1 n -1 -1 1 4 d p -1 2 f s f v 2 a -1 b -1 2 c s c v -1 8 q b a c v -1 2 s -1 n -1 j 0 n 2 j -1 n -1 d -1 p -1 2 f s f v n -1 j -1 -1 d p -1 2 f s f v 2 a z -1 2 b z -1 4 c s z 2 c v z 2 a -1 b -1 2 c s c v -1 1 2 -1 j -1 d p f v -1 2 s 2 a -1 b -1 2 c s c v z j 1 Binomial n j Gamma j 1 2 -1 -1 -1 d p -1 2 f s f v 2 a z -1 2 b z -1 4 c s z 2 c v z 2 4 a -1 b -1 2 c s c v -1 1 a b 2 c s -1 c v -1 d p 2 f s -1 f v 2 4 a b 2 c s -1 c v -1 b -1 a c v -1 2 s -1 n j 0 n 2 j -1 n p 2 f s -1 f v -1 d n -1 j d p 2 f s -1 f v 2 a z 2 b z 4 c s z -1 2 c v z 2 a b 2 c s -1 c v -1 1 2 -1 j -1 d -1 p f 2 s -1 v 2 a b 2 c s -1 c v z j 1 Binomial n j Gamma j 1 2 -1 d p 2 f s -1 f v 2 a z 2 b z 4 c s z -1 2 c v z 2 4 a b 2 c s -1 c v -1 1 a -1 b 2 c s -1 c v -1 1 4 d p 2 f s -1 f v 2 a -1 b 2 c s -1 c v -1 8 q 8 g 2 s -1 v b a 2 c s -1 c v -1 n j 0 n 2 j -1 n -1 d -1 p 2 f s -1 f v n -1 j -1 -1 d p 2 f s -1 f v 2 a z -1 2 b z 4 c s z -1 2 c v z 2 a -1 b 2 c s -1 c v -1 1 2 -1 j -1 d p f 2 s -1 v 2 a -1 b 2 c s -1 c v z j 1 Binomial n j Gamma j 1 2 -1 -1 -1 d p 2 f s -1 f v 2 a z -1 2 b z 4 c s z -1 2 c v z 2 4 a -1 b 2 c s -1 c v -1 n v SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["a_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["p_", " ", "z_"]], "+", "q_"]], "]"]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["c_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "v"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", 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["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]]]]], "-", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]]]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]]]]], "]"]]]]]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]]]]]]]]], "]"]]]]]]]]]], ")"]]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["q", "+", RowBox[List["2", " ", "g", " ", "s"]], "-", RowBox[List["g", " ", "v"]]]], ")"]]]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", "q"]], "+", RowBox[List["8", " ", "g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], "2"], RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]]]]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "s"]], "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "v"]]]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "+", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "+", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]]]]]]]]], "]"]]]]]]]], RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "+", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "+", RowBox[List["2", " ", "f", " ", "s"]], "-", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "+", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]]]]]]], "]"]]]]]]]], RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", "q"]], "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], "2"], RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]]]]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]], RowBox[List["1", "+", "j"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]]]]]]]]], "]"]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", "g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]]]], ")"]], "2"], RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]]]]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["2", RowBox[List["j", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]]]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "j"]], "+", "n"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "j"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]], "j"], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d"]], "+", "p", "-", RowBox[List["2", " ", "f", " ", "s"]], "+", RowBox[List["f", " ", "v"]], "+", RowBox[List["2", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]], "-", RowBox[List["4", " ", "c", " ", "s", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "v", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "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