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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Operations > Limit operation





http://functions.wolfram.com/05.09.25.0004.01









  


  








Input Form





Limit[GegenbauerC[n, \[Lambda], z]/(2 z)^n, z -> Infinity] == (1/n!) Pochhammer[\[Lambda], n]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["2", "z"]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]]]], ",", RowBox[List["z", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["n", "!"]]], RowBox[List["Pochhammer", "[", RowBox[List["\[Lambda]", ",", "n"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munder> <mi> lim </mi> <mrow> <mi> z </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msubsup> <mi> C </mi> <mi> n </mi> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <semantics> <msub> <mrow> <mo> ( </mo> <mi> &#955; </mi> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, &quot;\[Lambda]&quot;, &quot;)&quot;]], &quot;n&quot;], Pochhammer] </annotation> </semantics> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <limit /> <bvar> <ci> z </ci> </bvar> <condition> <apply> <tendsto /> <ci> z </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> C </ci> <ci> n </ci> </apply> <ci> &#955; </ci> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Pochhammer </ci> <ci> &#955; </ci> <ci> n </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "z_"]], ")"]], RowBox[List["-", "n_"]]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]]]], ",", RowBox[List["z_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Pochhammer", "[", RowBox[List["\[Lambda]", ",", "n"]], "]"]], RowBox[List["n", "!"]]]]]]]


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





2001-10-29