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JacobiND




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.32.06.0011.01









  


  








Input Form





JacobiND[z, m] \[Proportional] 1 + (1/2) Sin[z]^2 m - (1/32) Sin[z] (8 z Cos[z] - 11 Sin[z] + Sin[3 z]) m^2 + \[Ellipsis] /; (m -> 0)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiND", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Proportional]", RowBox[List["1", "+", RowBox[List[FractionBox["1", "2"], SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"], "m"]], "-", RowBox[List[FractionBox["1", "32"], " ", RowBox[List["Sin", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", "z", " ", RowBox[List["Cos", "[", "z", "]"]]]], "-", RowBox[List["11", " ", RowBox[List["Sin", "[", "z", "]"]]]], "+", RowBox[List["Sin", "[", RowBox[List["3", " ", "z"]], "]"]]]], ")"]], SuperscriptBox["m", "2"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["m", "\[Rule]", "0"]], ")"]]]]]]








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> nd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 32 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <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> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> JacobiND </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <apply> <sin /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 32 </cn> <apply> <sin /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <cos /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <sin /> <ci> z </ci> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> </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'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiND", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["1", "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"], " ", "m"]], "-", RowBox[List[FractionBox["1", "32"], " ", RowBox[List["Sin", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", "z", " ", RowBox[List["Cos", "[", "z", "]"]]]], "-", RowBox[List["11", " ", RowBox[List["Sin", "[", "z", "]"]]]], "+", RowBox[List["Sin", "[", RowBox[List["3", " ", "z"]], "]"]]]], ")"]], " ", SuperscriptBox["m", "2"]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["m", "\[Rule]", "0"]], ")"]]]]]]]]


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





2007-05-02