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

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2007-05-02