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Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving inverse hyperbolic functions > Involving cosh-1





http://functions.wolfram.com/01.22.21.0032.01









  


  










Input Form





Integrate[Coth[a ArcCosh[z]], z] == (1/(-2 + 8 a^2)) (((1 + 2 a) E^(ArcCosh[z] + 2 a ArcCosh[z]) Hypergeometric2F1[1 - 1/(2 a), 1, 2 - 1/(2 a), E^(2 a ArcCosh[z])] - (-1 + 2 a) (E^((3 + 2 a) ArcCosh[z]) Hypergeometric2F1[1 + 1/(2 a), 1, 2 + 1/(2 a), E^(2 a ArcCosh[z])] + (1 + 2 a) E^ArcCosh[z] (Hypergeometric2F1[-(1/(2 a)), 1, 1 - 1/(2 a), E^(2 a ArcCosh[z])] + E^(2 ArcCosh[z]) Hypergeometric2F1[1/(2 a), 1, 1 + 1/(2 a), E^(2 a ArcCosh[z])])))/E^(2 ArcCosh[z]))










Standard Form





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MathML Form







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<exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <arccosh /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <arccosh /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <arccosh /> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <arccosh /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18





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