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ArcCoth






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.28.16.0219.01









  


  










Input Form





ArcCoth[x] - ArcCsch[y] == ArcCoth[ (I (-1)^Floor[1/2 - Arg[((I Sqrt[1 + 1/y^2])/x - I/y)/Sqrt[1 - 1/x^2]]/Pi] (Sqrt[1 + 1/y^2] - 1/(x y)))/(Sqrt[1 - 1/x^2] Sqrt[1 - (Sqrt[1 + 1/y^2] - 1/(x y))^2/(1 - 1/x^2)])] - (1/2) I Pi (2 (1 + (-1)^Floor[1/2 - Arg[((I Sqrt[1 + 1/y^2])/x - I/y)/ Sqrt[1 - 1/x^2]]/Pi]) Floor[(Arg[(I - I/x)/Sqrt[1 - 1/x^2]] + Arg[Sqrt[1 + 1/y^2] + 1/y])/(2 Pi)] + (-1)^Floor[1/2 - Arg[((I Sqrt[1 + 1/y^2])/x - I/y)/Sqrt[1 - 1/x^2]]/Pi] + (-1)^(Floor[1/2 - Arg[((I Sqrt[1 + 1/y^2])/x - I/y)/Sqrt[1 - 1/x^2]]/ Pi] + Floor[-(Arg[1 - 1/x^2]/(2 Pi)) + Arg[1/(x y) - Sqrt[1 + 1/y^2]]/Pi + 1/2]) - 2 (-1 + (-1)^Floor[1/2 - Arg[((I Sqrt[1 + 1/y^2])/x - I/y)/ Sqrt[1 - 1/x^2]]/Pi]) Floor[1/2 - (Arg[(I - I/x)/Sqrt[1 - 1/x^2]] + Arg[Sqrt[1 + 1/y^2] + 1/y])/(2 Pi)])










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