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http://functions.wolfram.com/08.04.13.0004.01
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Wronskian[EllipticE[m], EllipticK[1 - m] - EllipticE[1 - m], m] == -(Pi/(4 m))
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["EllipticE", "[", "m", "]"]], ",", RowBox[List[RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m"]], "]"]], "-", RowBox[List["EllipticE", "[", RowBox[List["1", "-", "m"]], "]"]]]], ",", "m"]], "]"]], "\[Equal]", RowBox[List["-", FractionBox["\[Pi]", RowBox[List["4", " ", "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> <msub> <mi> W </mi> <mi> m </mi> </msub> <mo> ( </mo> <mrow> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mi> π </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> m </mi> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> m </ci> </apply> <apply> <ci> EllipticE </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["EllipticE", "[", "m_", "]"]], ",", RowBox[List[RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m_"]], "]"]], "-", RowBox[List["EllipticE", "[", RowBox[List["1", "-", "m_"]], "]"]]]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox["\[Pi]", RowBox[List["4", " ", "m"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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