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ArcCos






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.13.16.0147.01









  


  










Input Form





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