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 ArcCsch

 http://functions.wolfram.com/01.29.16.0161.01

 Input Form

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

 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