Jacobi elliptic function dn: Specific values (formula 09.29.03.0005)

JacobiDN

$Mathematica Notation$

Values at quarter-period points in the fundamental period parallelogram

http://functions.wolfram.com/09.29.03.0005.01

Input Form

JacobiDN[EllipticK[m], m] == Sqrt[1 - m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["EllipticK", "[", "m", "]"]], ",", "m"]], "]"]], "\[Equal]", SqrtBox[RowBox[List["1", "-", "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> dn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </msqrt> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiDN </ci> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["EllipticK", "[", "m_", "]"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", SqrtBox[RowBox[List["1", "-", "m"]]]]]]]

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

2001-10-29