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ArcTanh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Representations through equivalent functions > With related functions > Involving cos-1 > Involving tanh-1(z) > Involving tanh-1(z) and cos-1(((z2-1)1/2-z)1/2/(21/2(z2-1)1/4))





http://functions.wolfram.com/01.27.27.0479.01









  


  










Input Form





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