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





http://functions.wolfram.com/01.27.27.1904.01









  


  








Input Form





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