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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,z] > Operations > Limit operation





http://functions.wolfram.com/05.02.25.0001.01









  


  








Input Form





Limit[LaguerreL[n, z^2/(4 n)], n -> Infinity] == BesselJ[0, z]








Standard Form





Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", FractionBox[SuperscriptBox["z", "2"], RowBox[List["4", " ", "n"]]]]], "]"]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", RowBox[List["BesselJ", "[", RowBox[List["0", ",", "z"]], "]"]]]]]]]]








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> n </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> <msub> <mi> L </mi> <mi> n </mi> </msub> <mo> ( </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> n </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <msub> <mi> J </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <limit /> <bvar> <ci> n </ci> </bvar> <condition> <apply> <tendsto /> <ci> n </ci> <infinity /> </apply> </condition> <apply> <ci> LaguerreL </ci> <ci> n </ci> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> BesselJ </ci> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", FractionBox[SuperscriptBox["z_", "2"], RowBox[List["4", " ", "n_"]]]]], "]"]], ",", RowBox[List["n_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["BesselJ", "[", RowBox[List["0", ",", "z"]], "]"]]]]]]


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





2001-10-29