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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)/(2(z2-1)1/2))1/2)





http://functions.wolfram.com/01.27.27.0484.01









  


  








Input Form





ArcTanh[z] == -2 Sqrt[z^2] Sqrt[-(1/z^2)] ArcCos[Sqrt[(Sqrt[z^2 - 1] + z)/(2 Sqrt[z^2 - 1])]] + (1 - ((I Sqrt[-1 + z] z^(3/2))/(Sqrt[1 - z] Sqrt[z^2])) Sqrt[1/z] - Sqrt[z + 1] Sqrt[1/(z + 1)]) ((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