Jacobi elliptic function nc: Transformations (formula 09.31.16.0042)

JacobiNC

$Mathematica Notation$

Elliptic Functions

JacobiNC[z,m]

Transformations

Transformations and argument simplifications

Argument involving inverse Jacobi functions

http://functions.wolfram.com/09.31.16.0042.01

Input Form

JacobiNC[InverseJacobiCN[z, m], m] == 1/z

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["JacobiNC", "[", RowBox[List[RowBox[List["InverseJacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]], "\[Equal]", FractionBox["1", "z"]]]]]

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> nc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> cn </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiNC </ci> <apply> <ci> InverseJacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiNC", "[", RowBox[List[RowBox[List["InverseJacobiCN", "[", RowBox[List["z_", ",", "m_"]], "]"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", "z"]]]]]

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

2007-05-02