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

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</mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> x </mi> </mrow> <mo> + </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> &#8290; </mo> <mi> y </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msup> <mi> y </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </msqrt> </mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mi> y </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <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> <mo> + </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> - </mo> <mfrac> <mi> &#8520; </mi> <mi> y </mi> </mfrac> </mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mi> &#960; </mi> 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2007-05-02