Arg[ArcCsc[x + I y]] == ArcTan[ArcTan[(y + (x^2 + y^2) ((x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)/ (x^2 + y^2)^2)^(1/4) Cos[(1/2) ArcTan[1 + (-x^2 + y^2)/(x^2 + y^2)^2, (2 x y)/(x^2 + y^2)^2]])/(x^2 + y^2), (x + (x^2 + y^2) ((x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)/(x^2 + y^2)^2)^ (1/4) Sin[(1/2) ArcTan[1 + (-x^2 + y^2)/(x^2 + y^2)^2, (2 x y)/(x^2 + y^2)^2]])/(x^2 + y^2)], -Log[Sqrt[(y/(x^2 + y^2) + ((x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)/ (x^2 + y^2)^2)^(1/4) Cos[(1/2) ArcTan[1 + (-x^2 + y^2)/ (x^2 + y^2)^2, (2 x y)/(x^2 + y^2)^2]])^2 + (x/(x^2 + y^2) + ((x^4 + 2 x^2 (-1 + y^2) + (1 + y^2)^2)/(x^2 + y^2)^2)^ (1/4) Sin[(1/2) ArcTan[1 + (-x^2 + y^2)/(x^2 + y^2)^2, (2 x y)/(x^2 + y^2)^2]])^2]]]

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<mrow> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> x </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mfrac> <mrow> <msup> <mi> x </mi> <mn> 4 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> x </mi> <mn> 2 </mn> 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<apply> <plus /> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> x </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 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2001-10-29