InverseJacobiCD[-I, m] == EllipticK[m] + EllipticF[ArcSin[I], m]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> cd </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> F </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> &#8520; </mi> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> InverseJacobiCD </ci> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> m </ci> </apply> <apply> <plus /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <ci> EllipticF </ci> <apply> <arcsin /> <imaginaryi /> </apply> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29