Jacobi elliptic function ds: Representations through equivalent functions (formula 09.30.27.0025)

JacobiDS

$Mathematica Notation$

Elliptic Functions

JacobiDS[z,m]

Representations through equivalent functions

With related functions

Involving theta functions

http://functions.wolfram.com/09.30.27.0025.01

Input Form

JacobiDS[z, m] == NevilleThetaD[z, m]/NevilleThetaS[z, m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["JacobiDS", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", FractionBox[RowBox[List["NevilleThetaD", "[", RowBox[List["z", ",", "m"]], "]"]], RowBox[List["NevilleThetaS", "[", 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> ds </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <msub> <mi> ϑ </mi> <mi> d </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> ϑ </mi> <mi> s </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiDS </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <ci> NevilleThetaD </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <power /> <apply> <ci> NevilleThetaS </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiDS", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["NevilleThetaD", "[", RowBox[List["z", ",", "m"]], "]"]], RowBox[List["NevilleThetaS", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]

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

2001-10-29