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

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&#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <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> </mrow> <mo> + </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> y </mi> <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> </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> <ln /> <ci> y </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <floor /> <apply> <plus /> <cn 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2007-05-02