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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving cosh > Involving cosh(c z)(a+b coth(c z))beta





http://functions.wolfram.com/01.22.21.0401.01









  


  








Input Form





Integrate[Cosh[c z] (a + b Coth[c z])^\[Beta], z] == -(((b + (a + b)/(-1 + Coth[c z]))^\[Beta] ((-1 + \[Beta]) AppellF1[2 - \[Beta], 3/2, -\[Beta], 3 - \[Beta], -(2/(-1 + Coth[c z])), (a + b)/(b - b Coth[c z])] + (-2 + \[Beta]) AppellF1[1 - \[Beta], 3/2, -\[Beta], 2 - \[Beta], -(2/(-1 + Coth[c z])), (a + b)/(b - b Coth[c z])] (-1 + Coth[c z])) (a + b Coth[c z])^(-1 + \[Beta]) ((a + b Coth[c z])/(-1 + Coth[c z]))^ (1 - \[Beta]) Sinh[c z] Sqrt[Cosh[2 c z] + Sinh[2 c z]])/ (1 + (a + b)/(-b + b Coth[c z]))^\[Beta])/ (c (-2 + \[Beta]) (-1 + \[Beta]))








Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </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