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

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<mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> x </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> + </mo> <mfrac> <mi> &#8520; </mi> <mi> x </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> + </mo> <mfrac> <mi> &#8520; </mi> <mi> y </mi> </mfrac> </mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> </mrow> <mo> &#8971; </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <arcsec /> <ci> x </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <arccoth /> <ci> y </ci> </apply> </apply> </apply> <apply> 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</ci> </apply> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <floor /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <arg /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <arg /> <apply> <times /> <apply> <plus /> <imaginaryi /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02