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

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2007-05-02