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

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2007-05-02