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ArcTanh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Transformations > Related transformations > Differences involving the direct function > Involving log(z)





http://functions.wolfram.com/01.27.16.0178.01









  


  










Input Form





ArcTanh[x] - Log[y] == I Pi Floor[(-Arg[1 - x] + Arg[x + 1] + Pi)/(2 Pi)] - 2 I Pi (Floor[((1/2) Arg[(1 - x)/(x + 1)] - Arg[1/y] + Pi)/(2 Pi)] + Floor[((1/2) Im[Log[(1 - x)/(x + 1)]] + Pi)/(2 Pi)] + Floor[(Im[Log[y]] + Pi)/(2 Pi)]) + I Pi (1 - (-1)^Floor[Arg[1 + 1/(y Sqrt[(1 - x)/(x + 1)])]/(2 Pi) + 1/2]) + 2 ArcTanh[(1/(Sqrt[(1 - x)/(x + 1)] y) - 1)/ (1 + 1/(y Sqrt[(1 - x)/(x + 1)]))]










Standard Form





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MathML Form







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<cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





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