Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

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
 











JacobiNC






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiNC[z,m] > Series representations > Generalized power series > Expansions at m==0





http://functions.wolfram.com/09.31.06.0011.01









  


  










Input Form





JacobiNC[z, m] \[Proportional] Sec[z] + (1/4) ((-z) Sec[z] + Sin[z]) Tan[z] m - (1/512) Sec[z]^3 (-11 - 24 z^2 + 8 z^2 Cos[2 z] + 11 Cos[4 z] + 44 z Sin[2 z] + 4 z Sin[4 z]) m^2 + \[Ellipsis] /; (m -> 1)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiNC", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["Sec", "[", "z", "]"]], "+", RowBox[List[FractionBox["1", "4"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["Sec", "[", "z", "]"]]]], "+", RowBox[List["Sin", "[", "z", "]"]]]], ")"]], " ", RowBox[List["Tan", "[", "z", "]"]], "m"]], "-", RowBox[List[FractionBox["1", "512"], " ", SuperscriptBox[RowBox[List["Sec", "[", "z", "]"]], "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8", " ", SuperscriptBox["z", "2"], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["11", " ", RowBox[List["Cos", "[", RowBox[List["4", " ", "z"]], "]"]]]], "+", RowBox[List["44", " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]]]]]], ")"]], SuperscriptBox["m", "2"]]], " ", "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["m", "\[Rule]", "1"]], ")"]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> nc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mi> sec </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mi> sec </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> tan </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 512 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <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> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 44 </mn> <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> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <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> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 11 </mn> <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> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sec </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> JacobiNC </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <times /> <ci> sec </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <sin /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <sec /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <tan /> <ci> z </ci> </apply> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 512 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 44 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <sin /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -11 </cn> </apply> <apply> <power /> <apply> <sec /> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiNC", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Sec", "[", "z", "]"]], "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["Sec", "[", "z", "]"]]]], "+", RowBox[List["Sin", "[", "z", "]"]]]], ")"]], " ", RowBox[List["Tan", "[", "z", "]"]], " ", "m"]], "-", RowBox[List[FractionBox["1", "512"], " ", SuperscriptBox[RowBox[List["Sec", "[", "z", "]"]], "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8", " ", SuperscriptBox["z", "2"], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["11", " ", RowBox[List["Cos", "[", RowBox[List["4", " ", "z"]], "]"]]]], "+", RowBox[List["44", " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["4", " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["4", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox["m", "2"]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["m", "\[Rule]", "1"]], ")"]]]]]]]]










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





2007-05-02





© 1998-2014 Wolfram Research, Inc.