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

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</apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <floor /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <arg /> <apply> <times /> <apply> <plus /> <imaginaryi /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <arg /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 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2007-05-02