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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(2 (1-z2)1/2/-2+z2) > Involving tanh-1(2 (1-z2)1/2/-2+z2) and cosh-1(1/z)





http://functions.wolfram.com/01.27.27.2606.01









  


  








Input Form





ArcTanh[(2 Sqrt[1 - z^2])/(-2 + z^2)] == (-(Pi/(2 Sqrt[1 - z^2]))) ((-2 + z^2) Sqrt[z^4/(-1 + z^2)] Sqrt[(-1 + z^2)/z^4] Sqrt[(-1 + z^2)/(-2 + z^2)^2] - Sqrt[1 - 1/z^2] z (Sqrt[I/z] Sqrt[(-I) z] - Sqrt[-(I/z)] Sqrt[I z] + Sqrt[1/z^2] z - Sqrt[(-1 + z)/z] Sqrt[z/(-1 + z)] + Sqrt[1 + 1/z] Sqrt[z/(1 + z)])) - ((2 z)/Sqrt[1 - z^2]) Sqrt[1 - 1/z^2] (Pi/2 - ((Sqrt[-1 + z] Sqrt[z])/Sqrt[1 - z]) Sqrt[1/z] ArcCosh[1/z])








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