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ArcTanh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Representations through equivalent functions > With related functions > Involving sinh-1 > Involving tanh-1(z) > Involving tanh-1(z) and sinh-1(2 z/1-z2)





http://functions.wolfram.com/01.27.27.1899.01









  


  








Input Form





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








Standard Form





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MathML Form







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Rule Form





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





2003-08-21