Inverse of the Jacobi elliptic function cs: Representations through equivalent functions (formula 09.40.27.0002)

InverseJacobiDC

$Mathematica Notation$

Elliptic Functions

InverseJacobiDC[z,m]

Representations through equivalent functions

With related functions

Involving cd^-1

http://functions.wolfram.com/09.40.27.0002.01

Input Form

InverseJacobiDC[z, m] == InverseJacobiCD[1/z, m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["InverseJacobiDC", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List["InverseJacobiCD", "[", RowBox[List[FractionBox["1", "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> <msup> <mi> dc </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> <mrow> <msup> <mi> cd </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> InverseJacobiDC </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <ci> InverseJacobiCD </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiDC", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["InverseJacobiCD", "[", RowBox[List[FractionBox["1", "z"], ",", "m"]], "]"]]]]]]

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

2001-10-29