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ArcSec






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.18.16.0186.01









  


  










Input Form





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





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