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ArcTanh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Transformations > Related transformations > Differences involving the direct function > Involving cot-1(z)





http://functions.wolfram.com/01.27.16.0192.01









  


  








Input Form





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





2007-05-02