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

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<mrow> <msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <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> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mrow> <mi> x </mi> <mo> &#8290; </mo> <msqrt> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> 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2007-05-02