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ArcTanh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.27.26.0021.01









  


  










Input Form





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





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