Jacobi elliptic function cd: Transformations (formula 09.25.16.0021)

JacobiCD

$Mathematica Notation$

Elliptic Functions

JacobiCD[z,m]

Transformations

Transformations and argument simplifications

Argument involving half-periods

http://functions.wolfram.com/09.25.16.0021.01

Input Form

JacobiCD[z + 3 EllipticK[m], m] == JacobiSN[z, m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["JacobiCD", "[", RowBox[List[RowBox[List["z", "+", RowBox[List["3", RowBox[List["EllipticK", "[", "m", "]"]]]]]], ",", "m"]], "]"]], "\[Equal]", RowBox[List["JacobiSN", "[", RowBox[List["z", ",", "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> <mi> cd </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mi> sn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiCD </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiSN </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiCD", "[", RowBox[List[RowBox[List["z_", "+", RowBox[List["3", " ", RowBox[List["EllipticK", "[", "m_", "]"]]]]]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["JacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]

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

2007-05-02