Amplitude: Specific values (formula 09.24.03.0017)

JacobiAmplitude

$Mathematica Notation$

Derivatives with respect to m

For m==0

http://functions.wolfram.com/09.24.03.0017.01

Input Form

Derivative[0, 2][JacobiAmplitude][z, 0] == (1/128) (-20 z - 16 z Cos[2 z] + 16 Sin[2 z] + Sin[4 z])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["JacobiAmplitude", TagBox[RowBox[List["(", RowBox[List["0", ",", "2"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["z", ",", "0"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "128"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "20"]], " ", "z"]], "-", RowBox[List["16", " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["16", " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]]]], ")"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> am </mi> <semantics> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", RowBox[List["0", ",", "2"]], ")"]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 128 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 16 </mn> </mrow> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 20 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 2 </cn> </list> <ci> am </ci> </apply> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 128 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -16 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["JacobiAmplitude", TagBox[RowBox[List["(", RowBox[List["0", ",", "2"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["z_", ",", "0"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "128"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "20"]], " ", "z"]], "-", RowBox[List["16", " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["16", " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]]]], ")"]]]]]]]]

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

2007-05-02