Amplitude: Transformations (formula 09.24.16.0004)

JacobiAmplitude

$Mathematica Notation$

Elliptic Functions

JacobiAmplitude[z,m]

Transformations

Related transformations

http://functions.wolfram.com/09.24.16.0004.01

Input Form

Sin[JacobiAmplitude[z, m]] == JacobiSN[z, m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Sin", "[", RowBox[List["JacobiAmplitude", "[", RowBox[List["z", ",", "m"]], "]"]], "]"]], "\[Equal]", RowBox[List["JacobiSN", "[", 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> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> am </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> sn </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> <sin /> <apply> <ci> JacobiAmplitude </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <ci> JacobiSN </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sin", "[", RowBox[List["JacobiAmplitude", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["JacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]

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

2001-10-29