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

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</mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> b </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> </mrow> <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> <mi> &#960; </mi> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> y </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </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> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msup> <mrow> <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> <mrow> <mo> - </mo> <mfrac> <mi> a </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> b </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </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> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msup> <mrow> <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> ) 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2007-05-02