Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











JacobiAmplitude






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiAmplitude[z,m] > Specific values > Specialized values > Derivatives with respect to m > For m==0





http://functions.wolfram.com/09.24.03.0023.01









  


  










Input Form





Derivative[0, 8][JacobiAmplitude][z, 0] == (1/134217728) (-60474299760 z + 64 z (-1822886415 + 357215040 z^2 - 8096256 z^4 + 16384 z^6) Cos[2 z] - 1344 z (20225565 - 8302080 z^2 + 335872 z^4) Cos[4 z] - 72576 z (54545 - 26960 z^2 + 768 z^4) Cos[6 z] + 6720 z (-58671 + 24064 z^2) Cos[8 z] + 53760 z (-489 + 100 z^2) Cos[10 z] - 1068480 z Cos[12 z] - 20160 z Cos[14 z] - 448 (-163063575 + 157888080 z^2 - 9841920 z^4 + 77824 z^6) Sin[2 z] - 224 (-57287025 + 105953040 z^2 - 13486080 z^4 + 131072 z^6) Sin[4 z] + 120960 (13573 - 32100 z^2 + 4224 z^4) Sin[6 z] + 1680 (96087 - 221376 z^2 + 16384 z^4) Sin[8 z] - 80640 (-147 + 250 z^2) Sin[10 z] - 10080 (-61 + 48 z^2) Sin[12 z] + 20160 Sin[14 z] + 315 Sin[16 z])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["JacobiAmplitude", TagBox[RowBox[List["(", RowBox[List["0", ",", "8"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["z", ",", "0"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "134217728"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "60474299760"]], " ", "z"]], "+", RowBox[List["64", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1822886415"]], "+", RowBox[List["357215040", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["8096256", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["16384", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "z"]], "]"]]]], "-", RowBox[List["1344", " ", "z", " ", RowBox[List["(", RowBox[List["20225565", "-", RowBox[List["8302080", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["335872", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["4", " ", "z"]], "]"]]]], "-", RowBox[List["72576", " ", "z", " ", RowBox[List["(", RowBox[List["54545", "-", RowBox[List["26960", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["768", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["6", " ", "z"]], "]"]]]], "+", RowBox[List["6720", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "58671"]], "+", RowBox[List["24064", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["8", " ", "z"]], "]"]]]], "+", RowBox[List["53760", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "489"]], "+", RowBox[List["100", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["10", " ", "z"]], "]"]]]], "-", RowBox[List["1068480", " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["12", " ", "z"]], "]"]]]], "-", RowBox[List["20160", " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["14", " ", "z"]], "]"]]]], "-", RowBox[List["448", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "163063575"]], "+", RowBox[List["157888080", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["9841920", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["77824", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "-", RowBox[List["224", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "57287025"]], "+", RowBox[List["105953040", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["13486080", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["131072", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]]]], "+", RowBox[List["120960", " ", RowBox[List["(", RowBox[List["13573", "-", RowBox[List["32100", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4224", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["6", " ", "z"]], "]"]]]], "+", RowBox[List["1680", " ", RowBox[List["(", RowBox[List["96087", "-", RowBox[List["221376", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["16384", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["8", " ", "z"]], "]"]]]], "-", RowBox[List["80640", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "147"]], "+", RowBox[List["250", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["10", " ", "z"]], "]"]]]], "-", RowBox[List["10080", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "61"]], "+", RowBox[List["48", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["12", " ", "z"]], "]"]]]], "+", RowBox[List["20160", " ", RowBox[List["Sin", "[", RowBox[List["14", " ", "z"]], "]"]]]], "+", RowBox[List["315", " ", RowBox[List["Sin", "[", RowBox[List["16", " ", "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> 8 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;0&quot;, &quot;,&quot;, &quot;8&quot;]], &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 134217728 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 64 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 16384 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8096256 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 357215040 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 1822886415 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 1344 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 335872 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8302080 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 20225565 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 72576 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 768 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 26960 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 54545 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 6720 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 24064 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 58671 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 53760 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 100 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 489 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 1068480 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 20160 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 14 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 60474299760 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 448 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 77824 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 9841920 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 157888080 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 163063575 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 224 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 131072 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 13486080 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 105953040 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 57287025 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 120960 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4224 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 32100 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 13573 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 1680 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 16384 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 221376 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 96087 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 80640 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 250 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 147 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 10080 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 48 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 61 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 20160 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 14 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 315 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </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'> 8 </cn> </list> <ci> am </ci> </apply> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 134217728 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8096256 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 357215040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1822886415 </cn> </apply> <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'> 1344 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 335872 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8302080 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 20225565 </cn> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 72576 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 768 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 26960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 54545 </cn> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 6720 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 24064 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -58671 </cn> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 53760 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 100 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -489 </cn> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1068480 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20160 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 60474299760 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 448 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 77824 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9841920 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 157888080 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -163063575 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 224 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 131072 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 13486080 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 105953040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -57287025 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 120960 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4224 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 32100 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 13573 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1680 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 221376 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 96087 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 80640 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 250 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -147 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10080 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 48 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -61 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 20160 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 315 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> </apply> </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", ",", "8"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["z_", ",", "0"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "60474299760"]], " ", "z"]], "+", RowBox[List["64", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1822886415"]], "+", RowBox[List["357215040", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["8096256", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["16384", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "z"]], "]"]]]], "-", RowBox[List["1344", " ", "z", " ", RowBox[List["(", RowBox[List["20225565", "-", RowBox[List["8302080", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["335872", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["4", " ", "z"]], "]"]]]], "-", RowBox[List["72576", " ", "z", " ", RowBox[List["(", RowBox[List["54545", "-", RowBox[List["26960", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["768", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["6", " ", "z"]], "]"]]]], "+", RowBox[List["6720", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "58671"]], "+", RowBox[List["24064", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["8", " ", "z"]], "]"]]]], "+", RowBox[List["53760", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "489"]], "+", RowBox[List["100", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["10", " ", "z"]], "]"]]]], "-", RowBox[List["1068480", " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["12", " ", "z"]], "]"]]]], "-", RowBox[List["20160", " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["14", " ", "z"]], "]"]]]], "-", RowBox[List["448", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "163063575"]], "+", RowBox[List["157888080", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["9841920", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["77824", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "-", RowBox[List["224", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "57287025"]], "+", RowBox[List["105953040", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["13486080", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["131072", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]]]], "+", RowBox[List["120960", " ", RowBox[List["(", RowBox[List["13573", "-", RowBox[List["32100", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4224", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["6", " ", "z"]], "]"]]]], "+", RowBox[List["1680", " ", RowBox[List["(", RowBox[List["96087", "-", RowBox[List["221376", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["16384", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["8", " ", "z"]], "]"]]]], "-", RowBox[List["80640", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "147"]], "+", RowBox[List["250", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["10", " ", "z"]], "]"]]]], "-", RowBox[List["10080", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "61"]], "+", RowBox[List["48", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["12", " ", "z"]], "]"]]]], "+", RowBox[List["20160", " ", RowBox[List["Sin", "[", RowBox[List["14", " ", "z"]], "]"]]]], "+", RowBox[List["315", " ", RowBox[List["Sin", "[", RowBox[List["16", " ", "z"]], "]"]]]]]], "134217728"]]]]]










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





2007-05-02