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

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2007-05-02