Jacobi elliptic function dn: Representations through equivalent functions (formula 09.29.27.0078)

JacobiDN

$Mathematica Notation$

Elliptic Functions

JacobiDN[z,m]

Representations through equivalent functions

With related functions

Involving three other Jacobi elliptic functions

http://functions.wolfram.com/09.29.27.0078.01

Input Form

JacobiDN[z, m] == (JacobiDC[z, m] JacobiNC[z, m])/(1 + JacobiSC[z, m]^2)

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["JacobiDC", "[", RowBox[List["z", ",", "m"]], "]"]], " ", RowBox[List["JacobiNC", "[", RowBox[List["z", ",", "m"]], "]"]]]], RowBox[List["1", "+", SuperscriptBox[RowBox[List["JacobiSC", "[", RowBox[List["z", ",", "m"]], "]"]], "2"]]]]]]]]

MathML Form

<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> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mfrac> <mrow> <mrow> <mi> dc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> nc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mrow> <mi> sc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <ci> JacobiDC </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <ci> JacobiNC </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <ci> JacobiSC </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiDN", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["JacobiDC", "[", RowBox[List["z", ",", "m"]], "]"]], " ", RowBox[List["JacobiNC", "[", RowBox[List["z", ",", "m"]], "]"]]]], RowBox[List["1", "+", SuperscriptBox[RowBox[List["JacobiSC", "[", RowBox[List["z", ",", "m"]], "]"]], "2"]]]]]]]]

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

2007-05-02