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http://functions.wolfram.com/05.08.06.0026.01
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LaguerreL[n, \[Lambda], z] \[Proportional]
(\[Lambda]^n/n!) (1 + (n (1 + n - 2 z))/(2 \[Lambda]) +
((-1 + n) n (2 + 3 n^2 + n (5 - 12 z) + 12 (-2 + z) z))/
(24 \[Lambda]^2) + \[Ellipsis]) /; (Abs[\[Lambda]] -> Infinity)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[FractionBox[SuperscriptBox["\[Lambda]", "n"], RowBox[List["n", "!"]]], RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["n", " ", RowBox[List["(", RowBox[List["1", "+", "n", "-", RowBox[List["2", " ", "z"]]]], ")"]]]], RowBox[List["2", " ", "\[Lambda]"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "n"]], ")"]], " ", "n", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["3", " ", SuperscriptBox["n", "2"]]], "+", RowBox[List["n", " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["12", " ", "z"]]]], ")"]]]], "+", RowBox[List["12", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]], RowBox[List["24", " ", SuperscriptBox["\[Lambda]", "2"]]]], "+", "\[Ellipsis]"]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "\[Lambda]", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]
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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> <mrow> <msubsup> <mi> L </mi> <mi> n </mi> <mi> λ </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mfrac> <msup> <mi> λ </mi> <mi> n </mi> </msup> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mrow> <mi> n </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> λ </mi> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> n </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> n </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> - </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <msup> <mi> λ </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mo> … </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> λ </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> LaguerreL </ci> <ci> n </ci> <ci> λ </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <ci> λ </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> <times /> <ci> n </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> λ </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <ci> n </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> </apply> </apply> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -2 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <power /> <ci> λ </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> </apply> <apply> <ci> Rule </ci> <apply> <abs /> <ci> λ </ci> </apply> <infinity /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Lambda]", "n"], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["n", " ", RowBox[List["(", RowBox[List["1", "+", "n", "-", RowBox[List["2", " ", "z"]]]], ")"]]]], RowBox[List["2", " ", "\[Lambda]"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "n"]], ")"]], " ", "n", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["3", " ", SuperscriptBox["n", "2"]]], "+", RowBox[List["n", " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["12", " ", "z"]]]], ")"]]]], "+", RowBox[List["12", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]], RowBox[List["24", " ", SuperscriptBox["\[Lambda]", "2"]]]], "+", "\[Ellipsis]"]], ")"]]]], RowBox[List["n", "!"]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "\[Lambda]", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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