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ArcCosh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.26.16.0168.01









  


  










Input Form





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










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





© 1998- Wolfram Research, Inc.