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

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2007-05-02