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

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2007-05-02