Hyperbolic cosine integral: Integration (formula 01.20.21.1996)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving hyperbolic, exponential and trigonometric functions

Involving cos, sinh and exp

Involving e^{b z^r+d z+e} cos(a z^r+p z+q)sinh(w z^r+s z+t) cosh( c z^r+f z+g)

http://functions.wolfram.com/01.20.21.1996.01

Input Form

Integrate[E^(b z^2 + d z + e) Cos[a z^2 + p z + q] Sinh[w z^2 + s z + t] Cosh[c z^2 + f z + g], z] == (1/16) ((E^(e - g - I q - t - (d - f - I p - s)^2/(4 ((-I) a + b - c - w))) (d - f - I p - s + 2 ((-I) a + b - c - w) z) Gamma[1/2, -((d - f - I p - s + 2 ((-I) a + b - c - w) z)^2/ (4 ((-I) a + b - c - w)))])/(((-I) a + b - c - w) Sqrt[-((d - f - I p - s + 2 ((-I) a + b - c - w) z)^2/ ((-I) a + b - c - w))]) + (E^(e - g + I q - t - (d - f + I p - s)^2/(4 (I a + b - c - w))) (d - f + I p - s + 2 (I a + b - c - w) z) Gamma[1/2, -((d - f + I p - s + 2 (I a + b - c - w) z)^2/ (4 (I a + b - c - w)))])/((I a + b - c - w) Sqrt[-((d - f + I p - s + 2 (I a + b - c - w) z)^2/ (I a + b - c - w))]) + (E^(e + g - I q - t - (d + f - I p - s)^2/(4 ((-I) a + b + c - w))) (d + f - I p - s + 2 ((-I) a + b + c - w) z) Gamma[1/2, -((d + f - I p - s + 2 ((-I) a + b + c - w) z)^2/ (4 ((-I) a + b + c - w)))])/(((-I) a + b + c - w) Sqrt[-((d + f - I p - s + 2 ((-I) a + b + c - w) z)^2/ ((-I) a + b + c - w))]) + (E^(e + g + I q - t - (d + f + I p - s)^2/(4 (I a + b + c - w))) (d + f + I p - s + 2 (I a + b + c - w) z) Gamma[1/2, -((d + f + I p - s + 2 (I a + b + c - w) z)^2/ (4 (I a + b + c - w)))])/((I a + b + c - w) Sqrt[-((d + f + I p - s + 2 (I a + b + c - w) z)^2/ (I a + b + c - w))]) - (E^(e - g - I q + t - (d - f - I p + s)^2/(4 ((-I) a + b - c + w))) (d - f - I p + s + 2 ((-I) a + b - c + w) z) Gamma[1/2, -((d - f - I p + s + 2 ((-I) a + b - c + w) z)^2/ (4 ((-I) a + b - c + w)))])/(((-I) a + b - c + w) Sqrt[-((d - f - I p + s + 2 ((-I) a + b - c + w) z)^2/ ((-I) a + b - c + w))]) - (E^(e - g + I q + t - (d - f + I p + s)^2/(4 (I a + b - c + w))) (d - f + I p + s + 2 (I a + b - c + w) z) Gamma[1/2, -((d - f + I p + s + 2 (I a + b - c + w) z)^2/ (4 (I a + b - c + w)))])/((I a + b - c + w) Sqrt[-((d - f + I p + s + 2 (I a + b - c + w) z)^2/ (I a + b - c + w))]) - (E^(e + g - I q + t - (d + f - I p + s)^2/(4 ((-I) a + b + c + w))) (d + f - I p + s + 2 ((-I) a + b + c + w) z) Gamma[1/2, -((d + f - I p + s + 2 ((-I) a + b + c + w) z)^2/ (4 ((-I) a + b + c + w)))])/(((-I) a + b + c + w) Sqrt[-((d + f - I p + s + 2 ((-I) a + b + c + w) z)^2/ ((-I) a + b + c + w))]) - (E^(e + g + I q + t - (d + f + I p + s)^2/(4 (I a + b + c + w))) (d + f + I p + s + 2 (I a + b + c + w) z) Gamma[1/2, -((d + f + I p + s + 2 (I a + b + c + w) z)^2/ (4 (I a + b + c + w)))])/((I a + b + c + w) Sqrt[-((d + f + I p + s + 2 (I a + b + c + w) z)^2/(I a + b + c + w))]))

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]]], RowBox[List["Cos", "[", 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"]], "]"]], RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "16"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]]]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]]]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]]]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]]]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]]]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]]]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]]]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]]]]]]]], ")"]]]]]], ")"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> e </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> s </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> t </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> g </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 16 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mi> e </mi> <mo> - </mo> <mi> g </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> - </mo> <mi> t </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mi> e </mi> <mo> - </mo> <mi> g </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> - </mo> <mi> t </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> g </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> - </mo> <mi> t </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> g </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> - </mo> <mi> t </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> - </mo> <mi> w </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mi> e </mi> <mo> - </mo> <mi> g </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mi> t </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mi> e </mi> <mo> - </mo> <mi> g </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mi> t </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> g </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mi> t </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> g </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> + </mo> <mi> t </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mi> s </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> w </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> <ci> e </ci> </apply> </apply> <apply> <cos /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> p </ci> <ci> z </ci> </apply> <ci> q </ci> </apply> </apply> <apply> <sinh /> <apply> <plus /> <apply> <times /> <ci> w </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> s </ci> <ci> z </ci> </apply> <ci> t </ci> </apply> </apply> <apply> <cosh /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> <ci> g </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 16 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> g </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> q </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> t </ci> </apply> </apply> </apply> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> g </ci> </apply> <apply> <times /> <imaginaryi /> <ci> q </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> t </ci> </apply> </apply> </apply> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> e </ci> <ci> g </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> q </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> t </ci> </apply> </apply> </apply> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> e </ci> <ci> g </ci> <apply> <times /> <imaginaryi /> <ci> q </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> t </ci> </apply> </apply> </apply> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> g </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> q </ci> </apply> </apply> <ci> t </ci> </apply> </apply> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> g </ci> </apply> <apply> <times /> <imaginaryi /> <ci> q </ci> </apply> <ci> t </ci> </apply> </apply> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> e </ci> <ci> g </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> q </ci> </apply> </apply> <ci> t </ci> </apply> </apply> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> w </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> e </ci> <ci> g </ci> <apply> <times /> <imaginaryi /> <ci> q </ci> </apply> <ci> t </ci> </apply> </apply> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <ci> w </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]]], " ", RowBox[List["Cos", "[", 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_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "16"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "-", "w"]]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "-", "w"]]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "-", "w"]]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "-", "w"]]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "c", "+", "w"]]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "-", "c", "+", "w"]]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "+", "c", "+", "w"]]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]], "+", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]]]]]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", "c", "+", "w"]]]]]]]]]]], ")"]]]]]]]]

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

2002-12-18