Jacobi elliptic function dc: Transformations (formula 09.28.16.0003)

JacobiDC

$Mathematica Notation$

Elliptic Functions

JacobiDC[z,m]

Transformations

Transformations and argument simplifications

Argument involving basic arithmetic operations

http://functions.wolfram.com/09.28.16.0003.01

Input Form

JacobiDC[I z, 1 - m] == JacobiDN[z, m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["JacobiDC", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ",", RowBox[List["1", "-", "m"]]]], "]"]], "\[Equal]", RowBox[List["JacobiDN", "[", 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> dc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ❘ </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiDC </ci> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiDC", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z_"]], ",", RowBox[List["1", "-", "m_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]

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

2001-10-29