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

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<cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <times /> <ci> x </ci> <ci> y </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <plus /> <apply> <power /> <apply> <plus /> <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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <plus /> <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> y </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <pi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02