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ArcTanh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.27.27.3474.01









  


  










Input Form





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










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