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Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and exponential functions > Involving sinh and exp > Involving ep z sinh(b z) coth( c z)





http://functions.wolfram.com/01.22.21.0164.01









  


  










Input Form





Integrate[E^(p z) Sinh[b z] Coth[c z], z] == (1/4) ((2 E^((-b + p) z) Hypergeometric2F1[(-b + p)/(2 c), 1, (-b + 2 c + p)/(2 c), E^(2 c z)])/(-b + p) - (2 E^((b + p) z) Hypergeometric2F1[(b + p)/(2 c), 1, (b + 2 c + p)/(2 c), E^(2 c z)])/(b + p) + (2 E^((-b + 2 c + p) z) Hypergeometric2F1[(-b + 2 c + p)/(2 c), 1, (-b + 4 c + p)/(2 c), E^(2 c z)])/(-b + 2 c + p) - (2 E^((b + 2 c + p) z) Hypergeometric2F1[(b + 2 c + p)/(2 c), 1, (b + 4 c + p)/(2 c), E^(2 c z)])/(b + 2 c + p))










Standard Form





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MathML Form







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<apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <ci> p </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <ci> p </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> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <ci> p </ci> </apply> <cn type='integer'> -1 </cn> </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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