Jacobi elliptic function ns: Transformations (formula 09.33.16.0030)

JacobiNS

$Mathematica Notation$

Elliptic Functions

JacobiNS[z,m]

Transformations

Transformations and argument simplifications

Argument involving half-periods

http://functions.wolfram.com/09.33.16.0030.01

Input Form

JacobiNS[z - EllipticK[m], m] == -JacobiDC[z, m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["JacobiNS", "[", RowBox[List[RowBox[List["z", "-", RowBox[List["EllipticK", "[", "m", "]"]]]], ",", "m"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List["JacobiDC", "[", 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> <mrow> <mi> z </mi> <mo> - </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mrow> <mi> dc </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> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> </apply> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> JacobiDC </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[RowBox[List["z_", "-", RowBox[List["EllipticK", "[", "m_", "]"]]]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", RowBox[List["JacobiDC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]

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

2007-05-02