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ArcTanh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Representations through equivalent functions > With related functions > Involving csc-1 > Involving tanh-1(1/z1/2) > Involving tanh-1(1/z1/2) and csc-1((2(1-z)1/2/((1-z)1/2+(-z)1/2))1/2)





http://functions.wolfram.com/01.27.27.1351.01









  


  








Input Form





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