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http://functions.wolfram.com/09.29.03.0024.01
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JacobiDN[EllipticK[m] + 4 I EllipticK[1 - m], m] == Sqrt[1 - m]
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Cell[BoxData[RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List[RowBox[List["EllipticK", "[", "m", "]"]], "+", RowBox[List["4", "\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m"]], "]"]]]]]], ",", "m"]], "]"]], "\[Equal]", SqrtBox[RowBox[List["1", "-", "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> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </msqrt> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiDN </ci> <apply> <plus /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <imaginaryi /> <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> </apply> <ci> m </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List[RowBox[List["EllipticK", "[", "m_", "]"]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m_"]], "]"]]]]]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", SqrtBox[RowBox[List["1", "-", "m"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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