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ArcCsc






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsc[z] > Transformations > Related transformations > Sums involving the direct function > Involving tanh-1(z)





http://functions.wolfram.com/01.17.16.0143.01









  


  










Input Form





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










Standard Form





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MathML Form







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





2007-05-02





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