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ArcCoth






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Transformations > Products, sums, and powers of the direct function > Linear combinations of the direct function





http://functions.wolfram.com/01.28.16.0152.01









  


  










Input Form





a ArcCoth[x] + b ArcCoth[y] == I a Pi Floor[(-Arg[1 - 1/x] + Arg[1 + 1/x] + Pi)/(2 Pi)] - 2 I Pi (Floor[(-Arg[((1 - 1/x)/(1 + 1/x))^(-(a/2))] - Arg[(1 - 1/y)^(-(b/2))] + Pi)/(2 Pi)] + Floor[((1/2) Im[a Log[(1 - 1/x)/(1 + 1/x)]] + Pi)/(2 Pi)] + Floor[((1/2) Im[b Log[1 - 1/y]] + Pi)/(2 Pi)]) - 2 I Pi (Floor[(-Arg[1/(((1 - 1/x)/(1 + 1/x))^(a/2) (1 - 1/y)^(b/2))] - Arg[(1 + 1/y)^(b/2)] + Pi)/(2 Pi)] + Floor[(Pi - Im[Log[1/(((1 - 1/x)/(1 + 1/x))^(a/2) (1 - 1/y)^(b/2))]])/ (2 Pi)] + Floor[(Pi - (1/2) Im[b Log[1 + 1/y]])/(2 Pi)]) + I Pi (1 - (-1)^Floor[Arg[(1 + 1/y)^(b/2)/((1 - 1/y)^(b/2) ((1 - 1/x)/(1 + 1/x))^ (a/2)) + 1]/(2 Pi) + 1/2]) + 2 ArcCoth[((1 + 1/y)^(b/2)/((1 - 1/y)^(b/2) ((1 - 1/x)/(1 + 1/x))^(a/2)) + 1)/((1 + 1/y)^(b/2)/(((1 - 1/x)/(1 + 1/x))^(a/2) (1 - 1/y)^(b/2)) - 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