Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving powers of cos and exp > Involving eb zr+d z+e cosm(a zr+p z+q) sinh(c zr+f z+g)





http://functions.wolfram.com/01.19.21.1310.01









  


  










Input Form





Integrate[E^(b Sqrt[z] + d z + e) Cos[a Sqrt[z] + p z + q]^m Sinh[c Sqrt[z] + f z + g], z] == I 2^(-2 - m) E^(e - g + (I Pi)/2) Binomial[m, m/2] ((2 E^((b - c) Sqrt[z] + (d - f) z))/(d - f) + (2 E^(2 (g - (I Pi)/2) + (b + c) Sqrt[z] + (d + f) z))/(d + f) + Sqrt[Pi] (-(((b - c) Erfi[(b - c + 2 (d - f) Sqrt[z])/(2 Sqrt[d - f])])/ (E^((b - c)^2/(4 (d - f))) (d - f)^(3/2))) - ((b + c) E^(-((b + c)^2/(4 (d + f))) + 2 g - I Pi) Erfi[(b + c + 2 (d + f) Sqrt[z])/(2 Sqrt[d + f])])/(d + f)^(3/2))) (1 - Mod[m, 2]) + I 2^(-2 - m) Sum[Binomial[m, s] (E^(e - g + (I Pi)/2 - I q (m - 2 s)) ((2 E^(2 g - I Pi + 2 I q (m - 2 s) + (b + c + I a m - 2 I a s) Sqrt[z] + (d + f + I m p - 2 I p s) z))/(d + f + I m p - 2 I p s) + (2 E^((b - c - I a m + 2 I a s) Sqrt[z] + (d - f - I m p + 2 I p s) z))/(d - f - I m p + 2 I p s) - (E^(2 g - I Pi + 2 I q (m - 2 s) - (b + c + I a (m - 2 s))^2/ (4 (d + f + I m p - 2 I p s))) Sqrt[Pi] (b + c + I a (m - 2 s)) Erfi[(b + c + I a (m - 2 s) + 2 (d + f + I m p - 2 I p s) Sqrt[z])/ (2 Sqrt[d + f + I m p - 2 I p s])])/(d + f + I m p - 2 I p s)^ (3/2) - (Sqrt[Pi] (b - c - I a m + 2 I a s) Erfi[(b - c + I a (-m + 2 s) + 2 (d - f - I m p + 2 I p s) Sqrt[z])/(2 Sqrt[d - f - I m p + 2 I p s])])/ E^((b - c - I a m + 2 I a s)^2/(4 (d - f - I m p + 2 I p s)))/ (d - f - I m p + 2 I p s)^(3/2)) + E^(e + g - (I Pi)/2 - I q (m - 2 s)) ((2 E^(-2 g + I Pi + 2 I q (m - 2 s) + (b - c + I a m - 2 I a s) Sqrt[z] + (d - f + I m p - 2 I p s) z))/(d - f + I m p - 2 I p s) + (2 E^((b + c - I a m + 2 I a s) Sqrt[z] + (d + f - I m p + 2 I p s) z))/(d + f - I m p + 2 I p s) - (E^(-2 g + I Pi + 2 I q (m - 2 s) - (b - c + I a m - 2 I a s)^2/ (4 (d - f + I m p - 2 I p s))) Sqrt[Pi] (b - c + I a m - 2 I a s) Erfi[(b - c + I a (m - 2 s) + 2 (d - f + I m p - 2 I p s) Sqrt[z])/(2 Sqrt[d - f + I m p - 2 I p s])])/ (d - f + I m p - 2 I p s)^(3/2) - (Sqrt[Pi] (b + c - I a m + 2 I a s) Erfi[(b + c + I a (-m + 2 s) + 2 (d + f - I m p + 2 I p s) Sqrt[z])/(2 Sqrt[d + f - I m p + 2 I p s])])/E^((b + c - I a m + 2 I a s)^2/ (4 (d + f - I m p + 2 I p s)))/(d + f - I m p + 2 I p s)^ (3/2))), {s, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]]], SuperscriptBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["a", " ", SqrtBox["z"]]], "+", RowBox[List["p", " ", "z"]], "+", "q"]], "]"]], "m"], RowBox[List["Sinh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "-", "f"]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["g", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "+", "f"]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]]]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "-", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]]]]]]], "+", RowBox[List["2", " ", "g"]], "-", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "g"]], "-", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "g"]], "-", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], RowBox[List["3", "/", "2"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "-", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "g"]], "+", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "g"]], "+", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], RowBox[List["3", "/", "2"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "+", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> e </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mi> m </mi> </msup> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mi> p </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> g </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> - </mo> <mi> g </mi> <mo> + </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> m </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;m&quot;, Identity]], List[TagBox[FractionBox[&quot;m&quot;, &quot;2&quot;], Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mfrac> </mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> </msup> </mrow> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> g </mi> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mrow> </msup> </mrow> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8971; </mo> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mi> s </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;m&quot;, Identity]], List[TagBox[&quot;s&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> - </mo> <mi> g </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> q </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> </msup> </mrow> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> </mfrac> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> q </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mrow> </msup> </mrow> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> </mfrac> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> q </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> + </mo> <mi> g </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> q </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> </msup> </mrow> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> </mfrac> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> f </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> g </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> q </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mrow> </msup> </mrow> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> </mfrac> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> q </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> f </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> b </ci> </apply> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> <ci> e </ci> </apply> </apply> <apply> <power /> <apply> <cos /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <ci> p </ci> <ci> z </ci> </apply> <ci> q </ci> </apply> </apply> <ci> m </ci> </apply> <apply> <sinh /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> </apply> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> <ci> g </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> g </ci> </apply> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <imaginaryi /> <apply> <ci> Binomial </ci> <ci> m </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> d </ci> <ci> f </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> d </ci> <ci> f </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> g </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> f </ci> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <imaginaryi /> <apply> <sum /> <bvar> <ci> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> s </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <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> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <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> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> s </ci> </apply> </apply> </apply> <apply> <times /> <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> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <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> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> s </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <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> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <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> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> s </ci> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <ci> a </ci> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <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> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <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> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <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> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> q </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> s </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </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> b </ci> <ci> c </ci> <apply> <times /> <ci> a </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> q </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <ci> a </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <ci> a </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <ci> g </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> q </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> s </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> s </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> s </ci> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> <apply> <times /> <ci> a </ci> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> g </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> q </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> s </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <pi /> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </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> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> s </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> q </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <pi /> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> s </ci> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <ci> a </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> p </ci> <ci> s </ci> </apply> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </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_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["a_", " ", SqrtBox["z_"]]], "+", RowBox[List["p_", " ", "z_"]], "+", "q_"]], "]"]], "m_"], " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "-", "f"]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["g", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "+", "f"]]], "+", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]]]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "-", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "-", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]]]]]]], "+", RowBox[List["2", " ", "g"]], "-", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", "c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "g"]], "-", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "g"]], "-", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "-", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]]]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "g"]], "+", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "g"]], "+", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "q", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "-", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f", "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List["b", "+", "c", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "s"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", "c", "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f", "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "p", " ", "s"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]], ")"]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]]]]]]]]]]










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





2002-12-18