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

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</mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> x </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#8520; </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> &#8520; </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <arcsinh /> <ci> x </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> 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2007-05-02