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

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