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

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<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> <mfrac> <msup> <mrow> <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> <mi> &#8520; </mi> </msup> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> y </mi> </mrow> </msqrt> </mfrac> <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> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mrow> 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<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> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> log </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> </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> <mfrac> <mrow> <msup> <mrow> <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> 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type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02