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ArcTanh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Series representations > Residue representations





http://functions.wolfram.com/01.27.06.0018.01









  


  










Input Form





ArcTanh[z] == (-(z/2)) (Sum[Residue[((Gamma[s] Gamma[1 - s])/((-z^2)^s Gamma[3/2 - s])) Gamma[1/2 - s], {s, 1/2 + j}], {j, 0, Infinity}] + Sum[Residue[((Gamma[s] Gamma[1/2 - s])/((-z^2)^s Gamma[3/2 - s])) Gamma[1 - s], {s, 1 + j}], {j, 0, Infinity}]) /; Abs[z] > 1










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)





2001-10-29





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