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

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