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

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2007-05-02