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Csch




Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving powers of the direct function and hyperbolic functions > Involving power of coth > Involving cothmu(c z) sechnu(c z)





http://functions.wolfram.com/01.23.21.0425.01









  


  








Input Form





Integrate[Coth[c z]^u Csch[c z]^\[Nu], z] == (1/(c (u + \[Nu]))) (((1 - E^(2 c z))^(u + \[Nu]) Binomial[u, u/2] Csch[c z]^(u + \[Nu]) HypergeometricPFQ[{(u + \[Nu])/2, u + \[Nu]}, {1 + (u + \[Nu])/2}, E^(2 c z)] (1 - Mod[u, 2]))/2^u) + ((1 - E^(2 c z))^(u + \[Nu]) Csch[c z]^(u + \[Nu]) Sum[Binomial[u, k] (HypergeometricPFQ[{k + \[Nu]/2, u + \[Nu]}, {1 + k + \[Nu]/2}, E^(2 c z)]/(c (2 k + \[Nu]))/ E^(c (-2 k + u) z) + E^(c (-2 k + u) z) (HypergeometricPFQ[{-k + u + \[Nu]/2, u + \[Nu]}, {1 - k + u + \[Nu]/2}, E^(2 c z)]/(c (2 u - 2 k + \[Nu])))), {k, 0, Floor[(1/2) (-1 + u)]}])/2^u /; Element[u, Integers] && u > 0








Standard Form





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MathML Form







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</ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <ci> k </ci> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <ci> u </ci> <ci> &#957; </ci> </apply> </list> <list> <apply> <plus /> <ci> k </ci> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <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> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> u </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> u </ci> </apply> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <ci> u </ci> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <ci> u </ci> <ci> &#957; </ci> </apply> </list> <list> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <ci> u </ci> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <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> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <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> <plus /> <ci> u </ci> <ci> &#957; </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`u </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <csch /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> u </ci> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> u </ci> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <ci> u </ci> <apply> <times /> <ci> u </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <apply> <plus /> <ci> u </ci> <ci> &#957; </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <ci> u </ci> <ci> &#957; </ci> </apply> </list> <list> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> u </ci> <ci> &#957; 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Rule Form





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





2002-12-18