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

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2007-05-02