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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Series representations > Generalized power series > Expansions at lambda==infinity





http://functions.wolfram.com/05.09.06.0053.01









  


  








Input Form





GegenbauerC[n, \[Lambda], z] \[Proportional] (((2 z)^n \[Lambda]^n)/n!) (1 + O[1/\[Lambda]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["2", "z"]], ")"]], "n"], SuperscriptBox["\[Lambda]", "n"]]], RowBox[List["n", "!"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", "\[Lambda]"], "]"]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <mi> C </mi> <mi> n </mi> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mi> n </mi> </msup> </mrow> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mi> &#955; </mi> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> C </ci> <ci> n </ci> </apply> <ci> &#955; </ci> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <ci> n </ci> </apply> <apply> <power /> <ci> &#955; </ci> <ci> n </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GegenbauerC", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "z"]], ")"]], "n"], " ", SuperscriptBox["\[Lambda]", "n"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", "\[Lambda]"], "]"]]]], ")"]]]], RowBox[List["n", "!"]]]]]]]


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





2007-05-02