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

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2007-05-02