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

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</mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> y </mi> </mrow> <mrow> <mi> x </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> - </mo> <mfrac> <mi> &#8520; </mi> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> 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</mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mrow> <mi> x </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> x </mi> </mfrac> </mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> 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2007-05-02