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http://functions.wolfram.com/01.23.21.0053.01
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Integrate[z^n Sin[b z]^m Csch[c z], z] ==
2^(1 - m) E^(c z) Binomial[m, m/2] n! (-1 + Mod[m, 2])
Sum[(1/(-j + n)!) (-1)^j z^(-j + n) c^(-1 - j) HypergeometricPFQ[
{Subscript[a, 1], \[Ellipsis], Subscript[a, j + 1], 1},
{1 + Subscript[a, 1], \[Ellipsis], 1 + Subscript[a, j + 1]},
E^(2 c z)], {j, 0, n}] - 2^(1 - m) E^(c z) n!
Sum[(-1)^k Binomial[m, k] (E^((-(1/2)) I m Pi + I b (-2 k + m) z)
Sum[(1/(-j + n)!) (-1)^j z^(-j + n) (I b (-2 k + m) + c)^(-1 - j)
HypergeometricPFQ[{Subscript[b, 1], \[Ellipsis],
Subscript[b, j + 1], 1}, {1 + Subscript[b, 1], \[Ellipsis],
1 + Subscript[b, j + 1]}, E^(2 c z)], {j, 0, n}] +
E^((I m Pi)/2 - I b (-2 k + m) z) Sum[(1/(-j + n)!) (-1)^j z^(-j + n)
((-I) b (-2 k + m) + c)^(-1 - j) HypergeometricPFQ[
{Subscript[c, 1], \[Ellipsis], Subscript[c, j + 1], 1},
{1 + Subscript[c, 1], \[Ellipsis], 1 + Subscript[c, j + 1]},
E^(2 c z)], {j, 0, n}]), {k, 0, Floor[(1/2) (-1 + m)]}] /;
Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n + 1] ==
1/2 && Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] ==
Subscript[b, n + 1] == (c + I b (-2 k + m))/(2 c) &&
Subscript[c, 1] == Subscript[c, 2] == \[Ellipsis] == Subscript[c, n + 1] ==
(c - I b (-2 k + m))/(2 c) && Element[n, Integers] && n >= 0 &&
Element[m, Integers] && m > 0
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-1 </cn> <ci> j </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <imaginaryi /> <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> c </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> … </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <imaginaryi /> <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> c </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </list> <list> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <imaginaryi /> <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> c </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <ci> … </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <imaginaryi /> <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> c </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <ci> ℕ </ci> </apply> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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