ArcCoth[x] - I ArcSin[y] == ArcCoth[((-1)^Floor[1/2 - Arg[(-y - (I Sqrt[1 - y^2])/x)/Sqrt[1 - 1/x^2]]/ Pi] (-(y/x) - I Sqrt[1 - y^2]))/(Sqrt[1 - 1/x^2] Sqrt[1 - ((I y)/x - Sqrt[1 - y^2])^2/(1 - 1/x^2)])] + (1/2) I Pi (2 (1 + (-1)^Floor[1/2 - Arg[(-y - (I Sqrt[1 - y^2])/x)/Sqrt[1 - 1/x^2]]/ Pi]) Floor[(Arg[(I + I/x)/Sqrt[1 - 1/x^2]] + Arg[Sqrt[1 - y^2] - I y])/(2 Pi)] + (-1)^Floor[1/2 - Arg[(-y - (I Sqrt[1 - y^2])/x)/Sqrt[1 - 1/x^2]]/Pi] + (-1)^(Floor[-(Arg[1 - 1/x^2]/(2 Pi)) + Arg[(I y)/x - Sqrt[1 - y^2]]/Pi + 1/2] + Floor[1/2 - Arg[(-y - (I Sqrt[1 - y^2])/x)/Sqrt[1 - 1/x^2]]/ Pi]) - 2 (-1 + (-1)^Floor[1/2 - Arg[(-y - (I Sqrt[1 - y^2])/x)/Sqrt[1 - 1/x^2]]/ Pi]) Floor[1/2 - (Arg[(I + I/x)/Sqrt[1 - 1/x^2]] + Arg[Sqrt[1 - y^2] - I y])/(2 Pi)])

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2007-05-02