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

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2007-05-02