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

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