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ArcTanh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Representations through equivalent functions > With related functions > Involving cosh-1 > Involving tanh-1(1/z1/2) > Involving tanh-1(1/z1/2) and cosh-1(2 (-z)1/2/z-1)





http://functions.wolfram.com/01.27.27.2419.01









  


  








Input Form





ArcTanh[1/Sqrt[z]] == (Pi/8) (2 I (-1 + Sqrt[(-1 + z)/z] Sqrt[z/(-1 + z)] + (3 I z)/(2 Sqrt[-z^2])) (1 - ((z + 1)/(z - 1)) Sqrt[((z - 1)/(z + 1))^2]) + (z/Sqrt[-z^2]) (1 + ((z + 1)/(z - 1)) Sqrt[((z - 1)/(z + 1))^2])) + (1/4) (1 - ((z + 1)/(z - 1)) Sqrt[((z - 1)/(z + 1))^2] + Sqrt[1/(1 + z)] Sqrt[1 + z] (1 + ((z + 1)/(z - 1)) Sqrt[((z - 1)/(z + 1))^2])) ArcCosh[(2 Sqrt[-z])/(z - 1)] /; Abs[z] != 1








Standard Form





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MathML Form







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</apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> 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Rule Form





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





2003-08-21