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

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</mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> y </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msqrt> <mtext> </mtext> </mrow> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <mi> y </mi> </mrow> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> 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</mn> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mi> y </mi> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> x </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> <msqrt> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msqrt> </mrow> </mfrac> </mrow> <mo> ) 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</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> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> y </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 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<apply> <times /> <imaginaryi /> <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> <ci> x </ci> </apply> <ci> y </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <floor /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <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> 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2007-05-02