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

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