Amplitude: Primary definition (formula 09.24.02.0001)

JacobiAmplitude

$Mathematica Notation$

Elliptic Functions

JacobiAmplitude[z,m]

Primary definition

http://functions.wolfram.com/09.24.02.0001.01

Input Form

z == JacobiAmplitude[w, m] /; w == EllipticF[z, m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["z", "\[Equal]", RowBox[List["JacobiAmplitude", "[", RowBox[List["w", ",", "m"]], "]"]]]], "/;", RowBox[List["w", "\[Equal]", RowBox[List["EllipticF", "[", 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> z </mi> <mo> ⩵ </mo> <mrow> <mi> am </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> w </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> w </mi> <mo> ⩵ </mo> <mrow> <mi> F </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> <ci> Condition </ci> <apply> <eq /> <ci> z </ci> <apply> <ci> JacobiAmplitude </ci> <ci> w </ci> <ci> m </ci> </apply> </apply> <apply> <eq /> <ci> w </ci> <apply> <ci> EllipticF </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "z_", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["w", ",", "m"]], "]"]], "/;", RowBox[List["w", "\[Equal]", RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]]]

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

2001-10-29