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http://functions.wolfram.com/07.03.03.0006.01
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LaguerreL[\[Nu], \[Lambda], z] == Nest[#1 - D[#1, z] & , LaguerreL[\[Nu], z],
\[Lambda]] /; Element[\[Lambda], Integers] && \[Lambda] > 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Equal]", RowBox[List["Nest", "[", RowBox[List[RowBox[List[RowBox[List["#", "-", RowBox[List["D", "[", RowBox[List["#", ",", "z"]], "]"]]]], "&"]], ",", RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], ",", "\[Lambda]"]], "]"]]]], "/;", RowBox[List[RowBox[List["\[Lambda]", "\[Element]", "Integers"]], "\[And]", RowBox[List["\[Lambda]", ">", "0"]]]]]]]]
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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> ν </mi> <mi> λ </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> × </mo> <mrow> <mo> . </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mo> ∂ </mo> <mo> . </mo> </mrow> <mrow> <mo> ∂ </mo> <mi> z </mi> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> λ </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> L </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> λ </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msubsup> <mi> L </mi> <mi> ν </mi> <mi> λ </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> × </mo> <mrow> <mo> . </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mo> ∂ </mo> <mo> . </mo> </mrow> <mrow> <mo> ∂ </mo> <mi> z </mi> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> λ </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> L </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> λ </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]_", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Nest", "[", RowBox[List[RowBox[List[RowBox[List["#1", "-", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z"]]], "#1"]]]], "&"]], ",", RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], ",", "\[Lambda]"]], "]"]], "/;", RowBox[List[RowBox[List["\[Lambda]", "\[Element]", "Integers"]], "&&", RowBox[List["\[Lambda]", ">", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
