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http://functions.wolfram.com/01.20.21.2858.01
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Integrate[(E^(p z) Cosh[e z]^m Cosh[c z]^v)/(a + b E^(d z))^n, z] ==
(1/p) ((2^(-m - v) E^(p z) Binomial[m, m/2] Binomial[v, v/2]
Hypergeometric2F1[p/d, n, (d + p)/d, -((b E^(d z))/a)] (1 - Mod[m, 2])
(1 - Mod[v, 2]))/a^n) + (2^(-m - v) Binomial[v, v/2] (1 - Mod[v, 2])
Sum[(Binomial[m, k] ((-E^(((-e) (-2 k + m) + p) z)) (e (-2 k + m) + p)
Hypergeometric2F1[((-e) (-2 k + m) + p)/d, n,
(d - e (-2 k + m) + p)/d, -((b E^(d z))/a)] +
E^((e (-2 k + m) + p) z) (e (-2 k + m) - p) Hypergeometric2F1[
(e (-2 k + m) + p)/d, n, (d + e (-2 k + m) + p)/d,
-((b E^(d z))/a)]))/((e (-2 k + m) - p) (e (-2 k + m) + p)),
{k, 0, Floor[(1/2) (-1 + m)]}])/a^n +
(2^(-m - v) Binomial[m, m/2] (1 - Mod[m, 2])
Sum[(Binomial[v, s] ((-E^((p - c (-2 s + v)) z)) (p + c (-2 s + v))
Hypergeometric2F1[(p - c (-2 s + v))/d, n, (d + p - c (-2 s + v))/
d, -((b E^(d z))/a)] + E^((p + c (-2 s + v)) z)
(-p + c (-2 s + v)) Hypergeometric2F1[(p + c (-2 s + v))/d, n,
(d + p + c (-2 s + v))/d, -((b E^(d z))/a)]))/
((-p + c (-2 s + v)) (p + c (-2 s + v))),
{s, 0, Floor[(1/2) (-1 + v)]}])/a^n +
(2^(-m - v) Sum[Binomial[m, k] Sum[Binomial[v, s]
(((-E^((-2 e k + e m + p + 2 c s - c v) z)) (2 e k - e m + p -
2 c s + c v) Hypergeometric2F1[(-2 e k + e m + p + 2 c s - c v)/
d, n, (d - 2 e k + e m + p + 2 c s - c v)/d, -((b E^(d z))/
a)] + E^((2 e k - e m + p - 2 c s + c v) z)
(2 e k - e m - p - 2 c s + c v) Hypergeometric2F1[
(2 e k - e m + p - 2 c s + c v)/d, n, (d + 2 e k - e m + p -
2 c s + c v)/d, -((b E^(d z))/a)])/
((2 e k - e m - p - 2 c s + c v) (2 e k - e m + p - 2 c s +
c v)) + (E^((2 e k - e m + p + 2 c s - c v) z)
(2 e k - e m - p + 2 c s - c v) Hypergeometric2F1[
(2 e k - e m + p + 2 c s - c v)/d, n, (d + 2 e k - e m + p +
2 c s - c v)/d, -((b E^(d z))/a)] -
E^((-2 e k + e m + p - 2 c s + c v) z) (2 e k - e m + p + 2 c s -
c v) Hypergeometric2F1[(-2 e k + e m + p - 2 c s + c v)/d, n,
(d - 2 e k + e m + p - 2 c s + c v)/d, -((b E^(d z))/a)])/
((2 e k - e m - p + 2 c s - c v) (2 e k - e m + p + 2 c s -
c v))), {s, 0, Floor[(1/2) (-1 + v)]}],
{k, 0, Floor[(1/2) (-1 + m)]}])/a^n /; Element[n, Integers] && n > 0 &&
Element[m, Integers] && m > 0 && Element[v, Integers] && v > 0
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <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> <msup> <mi> cosh </mi> <mi> m </mi> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cosh </mi> <mi> v </mi> </msup> <mo> ( </mo> <mrow> <mi> c </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> <msup> <mi> ⅇ </mi> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> v </mi> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> v </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> v </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> 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</mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mi> a </mi> </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["e", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p"]], "d"], Hypergeometric2F1], ",", TagBox["n", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["d", "+", RowBox[List["e", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p"]], "d"], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", 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</mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> - </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mi> d </mi> </mfrac> <mo> , </mo> <mi> n </mi> </mrow> <mo> ; </mo> <mfrac> <mrow> <mi> d </mi> <mo> - </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mi> d </mi> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mi> a </mi> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", 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</mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> m </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> v </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mi> s </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> p </mi> </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> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mi> d </mi> </mfrac> <mo> , </mo> <mi> n </mi> </mrow> <mo> ; </mo> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mi> d </mi> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mi> a </mi> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> 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⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mi> d </mi> </mfrac> <mo> , </mo> <mi> n </mi> </mrow> <mo> ; </mo> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mi> d </mi> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mi> a </mi> </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["(", 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( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> v </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> 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</mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> e </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> e </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> p </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </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> 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</mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mi> d </mi> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mi> a </mi> </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[RowBox[List["-", "2"]], " ", "e", " ", "k"]], "+", RowBox[List["e", " ", "m"]], "+", "p", "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], "d"], Hypergeometric2F1], ",", TagBox["n", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["d", "-", RowBox[List["2", " ", "e", " ", "k"]], "+", RowBox[List["e", " ", "m"]], "+", "p", "+", RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], "d"], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]], "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> e </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> p </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> e </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> p </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> p </mi> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mi> v </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> a </mi> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> m </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> v </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <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> <mi> p </mi> <mi> d </mi> </mfrac> <mo> , </mo> <mi> n </mi> </mrow> <mo> ; </mo> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mi> p </mi> </mrow> <mi> d </mi> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mi> a </mi> </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["p", "d"], Hypergeometric2F1], ",", TagBox["n", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["d", "+", "p"]], "d"], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]], "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> v </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> n </mi> <mo> > </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> m </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> m </mi> <mo> > </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> v </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> v </mi> <mo> > </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <cosh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <ci> m </ci> </apply> <apply> <power /> <apply> <cosh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <ci> v </ci> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> v </ci> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> v </ci> <apply> <times /> <ci> v </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`v </ci> <cn type='integer'> 2 </cn> </apply> </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> <times /> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> k </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> e </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> e </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> e </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> n </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <ci> e </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> e </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> e </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> e </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> n </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> e </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> e </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> e </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </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> v </ci> </apply> </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> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> v </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> <times /> <apply> <ci> Binomial </ci> <ci> v </ci> <ci> s </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> n </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> 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d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> n </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s 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<power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> k </ci> </apply> <apply> <sum /> <bvar> <ci> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> v </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <ci> v </ci> <ci> s </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> e </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s 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e </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> e </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> n </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> e </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> e </ci> <ci> k </ci> </apply> <apply> <times /> <ci> e </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> e </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> e </ci> <ci> k </ci> </apply> <apply> <times /> <ci> e </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v 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/> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> e </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> e </ci> <ci> m </ci> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </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> v </ci> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <ci> z </ci> </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> <ci> Binomial </ci> <ci> v </ci> <apply> <times /> <ci> v </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 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