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

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<mo> - </mo> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mi> &#960; </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> <mo> + </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> 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<mi> x </mi> </mrow> <mo> + </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> y </mi> </mrow> </msqrt> </mrow> <msqrt> <mrow> <mi> y </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> </mrow> <mo> &#8971; </mo> </mrow> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> &#8970; </mo> <mrow> <mfrac> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> + </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - 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2007-05-02