Jacobi elliptic function ns: Representations through equivalent functions (formula 09.33.27.0012)

JacobiNS

$Mathematica Notation$

Elliptic Functions

JacobiNS[z,m]

Representations through equivalent functions

With related functions

Involving two other Jacobi elliptic functions

Involving ds and nd

http://functions.wolfram.com/09.33.27.0012.01

Input Form

JacobiNS[z, m] == JacobiND[z, m] JacobiDS[z, m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["JacobiNS", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["JacobiND", "[", RowBox[List["z", ",", "m"]], "]"]], " ", RowBox[List["JacobiDS", "[", 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> ns </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> nd </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> ds </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiNS </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <ci> JacobiND </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <ci> JacobiDS </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiNS", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["JacobiND", "[", RowBox[List["z", ",", "m"]], "]"]], " ", RowBox[List["JacobiDS", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]

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

2001-10-29