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

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