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Mathematica Notation

Traditional Notation

Elliptic Functions > JacobiDN[z,m] > Transformations > Sums over products of four Jacobi functions




Input Form

JacobiDN[z, m]^2 JacobiDN[z + EllipticK[m], m]^2 == 1 - m

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "2"], SuperscriptBox[RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z", "+", RowBox[List["EllipticK", "[", "m", "]"]]]], ",", "m"]], "]"]], "2"]]], "\[Equal]", RowBox[List["1", "-", "m"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mrow> <mi> dn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mi> dn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> + </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <power /> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> JacobiDN </ci> <apply> <plus /> <ci> z </ci> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["JacobiDN", "[", RowBox[List["z_", ",", "m_"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["z_", "+", RowBox[List["EllipticK", "[", "m_", "]"]]]], ",", "m_"]], "]"]], "2"]]], "]"]], "\[RuleDelayed]", RowBox[List["1", "-", "m"]]]]]]


A. Khare, U. Sukhatme, "Cyclic Identities Involving Jacobi Elliptic Functions", math-ph/0201004, (2002) http://arXiv.org/abs/math-ph/0201004

A. Khare, U. Sukhatme, "Cyclic Identities Involving Jacobi Elliptic Functions", Journal of Mathematical Physics, v. 43, issue 7, pp. 3798-3806 (2002)

Date Added to functions.wolfram.com (modification date)