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

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