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http://functions.wolfram.com/01.24.21.0246.01
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Integrate[E^(p z) Sin[a z]^m Sinh[b z]^u Sech[c z], z] ==
(1/(c + p)) I^u 2^(1 - m - u) E^((c + p) z) Binomial[m, m/2]
Binomial[u, u/2] Hypergeometric2F1[(c + p)/(2 c), 1, (3 c + p)/(2 c),
-E^(2 c z)] (1 - Mod[m, 2]) (1 - Mod[u, 2]) +
I^u 2^(1 - m - u) Binomial[u, u/2] (1 - Mod[u, 2])
Sum[(-1)^k Binomial[m, k] ((E^((I m Pi)/2 + (c + 2 I a k - I a m + p) z)
Hypergeometric2F1[1, (c + 2 I a k - I a m + p)/(2 c),
(3 c + 2 I a k - I a m + p)/(2 c), -E^(2 c z)])/
(c + 2 I a k - I a m + p) +
(E^((-(1/2)) I m Pi + (c - 2 I a k + I a m + p) z)
Hypergeometric2F1[1, (c - 2 I a k + I a m + p)/(2 c),
(3 c - 2 I a k + I a m + p)/(2 c), -E^(2 c z)])/
(c - 2 I a k + I a m + p)), {k, 0, Floor[(1/2) (-1 + m)]}] +
2^(1 - m - u) Binomial[m, m/2] (1 - Mod[m, 2])
Sum[(-1)^j Binomial[u, j] (((-1)^u E^((c + 2 b j + p - b u) z)
Hypergeometric2F1[1, (c + 2 b j + p - b u)/(2 c),
(3 c + 2 b j + p - b u)/(2 c), -E^(2 c z)])/(c + 2 b j + p - b u) +
(E^((c - 2 b j + p + b u) z) Hypergeometric2F1[1,
(c - 2 b j + p + b u)/(2 c), (3 c - 2 b j + p + b u)/(2 c),
-E^(2 c z)])/(c - 2 b j + p + b u)),
{j, 0, Floor[(1/2) (-1 + u)]}] + 2^(1 - m - u)
Sum[(-1)^k Binomial[m, k] Sum[(-1)^j Binomial[u, j]
(((-1)^u E^((1/2) I Pi m + (c + 2 b j + 2 I a k - I a m + p - b u) z)
Hypergeometric2F1[1, (c + 2 b j + 2 I a k - I a m + p - b u)/
(2 c), (3 c + 2 b j + 2 I a k - I a m + p - b u)/(2 c),
-E^(2 c z)])/(c + 2 b j + 2 I a k - I a m + p - b u) +
((-1)^u E^((-(1/2)) I Pi m + (c + 2 b j - 2 I a k + I a m + p - b u)
z) Hypergeometric2F1[1, (c + 2 b j - 2 I a k + I a m + p - b u)/
(2 c), (3 c + 2 b j - 2 I a k + I a m + p - b u)/(2 c),
-E^(2 c z)])/(c + 2 b j - 2 I a k + I a m + p - b u) +
(E^((1/2) I Pi m + (c - 2 b j + 2 I a k - I a m + p + b u) z)
Hypergeometric2F1[1, (c - 2 b j + 2 I a k - I a m + p + b u)/
(2 c), (3 c - 2 b j + 2 I a k - I a m + p + b u)/(2 c),
-E^(2 c z)])/(c - 2 b j + 2 I a k - I a m + p + b u) +
(E^((-(1/2)) I Pi m + (c - 2 b j - 2 I a k + I a m + p + b u) z)
Hypergeometric2F1[1, (c - 2 b j - 2 I a k + I a m + p + b u)/
(2 c), (3 c - 2 b j - 2 I a k + I a m + p + b u)/(2 c),
-E^(2 c z)])/(c - 2 b j - 2 I a k + I a m + p + b u)),
{j, 0, Floor[(1/2) (-1 + u)]}], {k, 0, Floor[(1/2) (-1 + m)]}] /;
Element[m, Integers] && m > 0 && Element[u, Integers] && u > 0
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<mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> <mo> - </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> u </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> </mrow> </mfrac> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> <mo> - </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> u </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> </mrow> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </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["1", Hypergeometric2F1], ",", TagBox[FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", "b", " ", "j"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], "+", "p", "-", RowBox[List["b", " ", "u"]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["3", " ", "c"]], "+", RowBox[List["2", " ", "b", 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<times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> u </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <ci> Binomial </ci> <ci> u </ci> <ci> j </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> k </ci> </apply> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> u </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <ci> Binomial </ci> <ci> u </ci> <ci> j </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <imaginaryi /> <pi /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <imaginaryi /> <pi /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> u </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> m </ci> <integers /> </apply> <apply> <in /> <ci> u </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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