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ArcCosh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.26.16.0205.01









  


  










Input Form





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