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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,z] > Limit representations





http://functions.wolfram.com/07.13.09.0001.01









  


  








Input Form





GegenbauerC[\[Nu], z] == Limit[(1/\[Lambda]) GegenbauerC[\[Nu], \[Lambda], z], \[Lambda] -> 0]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[FractionBox["1", "\[Lambda]"], RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", "\[Lambda]", ",", "z"]], "]"]]]], ",", RowBox[List["\[Lambda]", "\[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> <msubsup> <mi> C </mi> <mi> &#957; </mi> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> &#955; </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mfrac> <mn> 1 </mn> <mi> &#955; </mi> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <mi> C </mi> <mi> &#957; </mi> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> GegenbauerC </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> <apply> <limit /> <bvar> <ci> &#955; </ci> </bvar> <condition> <apply> <tendsto /> <ci> &#955; </ci> <cn type='integer'> 0 </cn> </apply> </condition> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> C </ci> <ci> &#957; </ci> </apply> <ci> &#955; </ci> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Lambda]"], ",", RowBox[List["\[Lambda]", "\[Rule]", "0"]]]], "]"]]]]]]


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





2001-10-29