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

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2007-05-02