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





http://functions.wolfram.com/01.27.27.2244.01









  


  










Input Form





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