|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/01.20.21.4706.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Integrate[(E^(p z) Cosh[d z])/(a + b Sinh[e z] + c Cosh[e z])^2, z] ==
(1/2) ((E^((-d + e + p) z) ((-a) (a + Sqrt[a^2 + b^2 - c^2])
Hypergeometric2F1[(-d + e + p)/e, 1, 2 + (-d + p)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] +
a (a - Sqrt[a^2 + b^2 - c^2]) Hypergeometric2F1[(-d + e + p)/e, 1,
2 + (-d + p)/e, -(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] +
a^2 Hypergeometric2F1[(-d + e + p)/e, 2, 2 + (-d + p)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] +
b^2 Hypergeometric2F1[(-d + e + p)/e, 2, 2 + (-d + p)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] -
c^2 Hypergeometric2F1[(-d + e + p)/e, 2, 2 + (-d + p)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] +
a Sqrt[a^2 + b^2 - c^2] Hypergeometric2F1[(-d + e + p)/e, 2,
2 + (-d + p)/e, ((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] -
a^2 Hypergeometric2F1[(-d + e + p)/e, 2, 2 + (-d + p)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] -
b^2 Hypergeometric2F1[(-d + e + p)/e, 2, 2 + (-d + p)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] +
c^2 Hypergeometric2F1[(-d + e + p)/e, 2, 2 + (-d + p)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] +
a Sqrt[a^2 + b^2 - c^2] Hypergeometric2F1[(-d + e + p)/e, 2,
2 + (-d + p)/e, -(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))]))/
((b - c) (a^2 + b^2 - c^2)^(3/2) (-d + e + p)) +
(E^((d + e + p) z) ((-a) (a + Sqrt[a^2 + b^2 - c^2])
Hypergeometric2F1[(d + e + p)/e, 1, 2 + (d + p)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] +
a (a - Sqrt[a^2 + b^2 - c^2]) Hypergeometric2F1[(d + e + p)/e, 1,
2 + (d + p)/e, -(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] +
a^2 Hypergeometric2F1[(d + e + p)/e, 2, 2 + (d + p)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] +
b^2 Hypergeometric2F1[(d + e + p)/e, 2, 2 + (d + p)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] -
c^2 Hypergeometric2F1[(d + e + p)/e, 2, 2 + (d + p)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] +
a Sqrt[a^2 + b^2 - c^2] Hypergeometric2F1[(d + e + p)/e, 2,
2 + (d + p)/e, ((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] -
a^2 Hypergeometric2F1[(d + e + p)/e, 2, 2 + (d + p)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] -
b^2 Hypergeometric2F1[(d + e + p)/e, 2, 2 + (d + p)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] +
c^2 Hypergeometric2F1[(d + e + p)/e, 2, 2 + (d + p)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] +
a Sqrt[a^2 + b^2 - c^2] Hypergeometric2F1[(d + e + p)/e, 2,
2 + (d + p)/e, -(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))]))/
((b - c) (a^2 + b^2 - c^2)^(3/2) (d + e + p)))
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], RowBox[List["Cosh", "[", RowBox[List["d", " ", "z"]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]]]], "+", RowBox[List["c", " ", RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]]]]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "1", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["a", "-", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "1", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], ")"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["d", "+", "e", "+", "p"]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "1", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["a", "-", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "1", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["d", "+", "e", "+", "p"]], ")"]]]], ")"]]]]]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> d </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["p", "-", "d"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> d </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["p", "-", "d"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> d </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["p", "-", "d"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> d </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["p", "-", "d"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> d </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["p", "-", "d"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> d </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["p", "-", "d"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> d </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["p", "-", "d"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> d </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["p", "-", "d"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> d </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["p", "-", "d"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mi> d </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["p", "-", "d"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </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> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["d", "+", "p"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["d", "+", "p"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["d", "+", "p"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["d", "+", "p"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["d", "+", "p"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["d", "+", "p"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["d", "+", "p"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> - </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["d", "+", "p"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], "-", "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["d", "+", "p"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> e </mi> </mfrac> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["d", "+", "p"]], "e"], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </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> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mi> e </mi> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </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> <times /> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <cosh /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <sinh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <cosh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </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> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <ci> e </ci> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </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> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> d </ci> <ci> e </ci> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", "z_"]]], " ", RowBox[List["Cosh", "[", RowBox[List["d_", " ", "z_"]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Sinh", "[", RowBox[List["e_", " ", "z_"]], "]"]]]], "+", RowBox[List["c_", " ", RowBox[List["Cosh", "[", RowBox[List["e_", " ", "z_"]], "]"]]]]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "1", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["a", "-", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "1", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List[RowBox[List["-", "d"]], "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", "e", "+", "p"]], ")"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["d", "+", "e", "+", "p"]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["(", RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "1", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["a", "-", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "1", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List[RowBox[List["-", "a"]], "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]], "+", RowBox[List["a", " ", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["d", "+", "e", "+", "p"]], "e"], ",", "2", ",", RowBox[List["2", "+", FractionBox[RowBox[List["d", "+", "p"]], "e"]]], ",", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", " ", "z"]]]]], RowBox[List["a", "+", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["d", "+", "e", "+", "p"]], ")"]]]]]]], ")"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|