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

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2007-05-02