ArcCoth[x] - I ArcSec[y] == ArcCoth[((-1)^Floor[1/2 - Arg[(1/y - (I Sqrt[1 - 1/y^2])/x)/Sqrt[1 - 1/x^2]]/ Pi] ((-I) Sqrt[1 - 1/y^2] + 1/(x y)))/(Sqrt[1 - 1/x^2] Sqrt[1 - (-Sqrt[1 - 1/y^2] - I/(x y))^2/(1 - 1/x^2)])] + (1/2) Pi I (-1 + (-1)^(Floor[1/2 - Arg[(1/y - (I Sqrt[1 - 1/y^2])/x)/Sqrt[1 - 1/x^2]]/ Pi] + Floor[1/2 - Arg[1 - 1/x^2]/(2 Pi) + Arg[-Sqrt[1 - 1/y^2] - I/(x y)]/Pi]) + 2 (1 + (-1)^Floor[1/2 - Arg[(1/y - (I Sqrt[1 - 1/y^2])/x)/ Sqrt[1 - 1/x^2]]/Pi]) Floor[(Arg[(I + I/x)/Sqrt[1 - 1/x^2]] + Arg[Sqrt[1 - 1/y^2] + I/y])/(2 Pi)] + (-1)^Floor[1/2 - Arg[(1/y - (I Sqrt[1 - 1/y^2])/x)/Sqrt[1 - 1/x^2]]/Pi] - 2 (-1 + (-1)^Floor[1/2 - Arg[(1/y - (I Sqrt[1 - 1/y^2])/x)/ Sqrt[1 - 1/x^2]]/Pi]) Floor[1/2 - (Arg[(I + I/x)/Sqrt[1 - 1/x^2]] + Arg[Sqrt[1 - 1/y^2] + I/y])/(2 Pi)])

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