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ArcTanh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/01.27.26.0017.01









  


  








Input Form





ArcTanh[z] - (Pi/4) (Sqrt[-(1/z^2)] z + I (Sqrt[1/(1 - z)] Sqrt[1 - z] - Sqrt[1 - 1/z] Sqrt[z/(z - 1)] + (I Sqrt[-z^2])/z + Sqrt[1 + 1/z] Sqrt[z/(z + 1)] - Sqrt[1/(z + 1)] Sqrt[z + 1])) - Sum[z^(-2 k - 1)/(2 k + 1), {k, 0, n}] == (((-1)^n z Sqrt[-(z^2)^(-1)])/2) MeijerG[{{1, 3/2 + n, 1/2}, {}}, {{3/2 + n}, {0, 1/2}}, -(1/z^2)] /; Element[n, Integers] && n >= 0








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