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 | | http://functions.wolfram.com/05.08.25.0001.01 | 
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 | | Limit[(1/n^\[Lambda]) LaguerreL[n, \[Lambda], z^2/(4 n)], n -> Infinity] == 
 (2^\[Lambda] BesselJ[\[Lambda], z])/z^\[Lambda] | 
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 | | Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox["n", "\[Lambda]"]], RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "\[Lambda]", ",", FractionBox[SuperscriptBox["z", "2"], RowBox[List["4", " ", "n"]]]]], "]"]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["2", "\[Lambda]"], " ", SuperscriptBox["z", RowBox[List["-", "\[Lambda]"]]], " ", RowBox[List["BesselJ", "[", RowBox[List["\[Lambda]", ",", "z"]], "]"]]]]]]]]]] | 
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   <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> → </mo>  <annotation encoding='Mathematica'> "\[Rule]" </annotation>  </semantics>  <mi> ∞ </mi>  </mrow>  </munder>  <mo> ⁢ </mo>  <mtext>   </mtext>  <mrow>  <mfrac>  <mn> 1 </mn>  <msup>  <mi> n </mi>  <mi> λ </mi>  </msup>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <msubsup>  <mi> L </mi>  <mi> n </mi>  <mi> λ </mi>  </msubsup>  <mo> ( </mo>  <mfrac>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> n </mi>  </mrow>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mrow>  <msup>  <mn> 2 </mn>  <mi> λ </mi>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mo> - </mo>  <mi> λ </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <msub>  <mi> J </mi>  <mi> λ </mi>  </msub>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </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>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <ci> n </ci>  <ci> λ </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <ci> LaguerreL </ci>  <ci> n </ci>  <ci> λ </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>  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <ci> λ </ci>  </apply>  <apply>  <power />  <ci> z </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> λ </ci>  </apply>  </apply>  <apply>  <ci> BesselJ </ci>  <ci> λ </ci>  <ci> z </ci>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", FractionBox[SuperscriptBox["z_", "2"], RowBox[List["4", " ", "n_"]]]]], "]"]], SuperscriptBox["n_", "\[Lambda]_"]], ",", RowBox[List["n_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", "\[Lambda]"], " ", SuperscriptBox["z", RowBox[List["-", "\[Lambda]"]]], " ", RowBox[List["BesselJ", "[", RowBox[List["\[Lambda]", ",", "z"]], "]"]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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