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http://functions.wolfram.com/05.02.11.0002.01
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LaguerreL[n, z] == ((-1)^n/n!) Sum[(1/k!) Nest[-D[z D[#1, z], z] & , z^n, k],
{k, 0, n}]
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Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], RowBox[List["n", "!"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[FractionBox["1", RowBox[List["k", "!"]]], RowBox[List["Nest", "[", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["(", RowBox[List["z", " ", RowBox[List[SubscriptBox["\[PartialD]", "z"], "#"]]]], ")"]]]]]], "&"]], ",", SuperscriptBox["z", "n"], ",", "k"]], "]"]]]]]]]]]]]]
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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> <msub> <mi> L </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mo> ∂ </mo> <mrow> <mo> ∂ </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mfrac> <mrow> <mo> ∂ </mo> <mo> . </mo> </mrow> <mrow> <mo> ∂ </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> n </mi> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> L </ms> <ms> n </ms> </apply> <ms> ( </ms> <ms> z </ms> <ms> ) </ms> </list> </apply> <ms> ⩵ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> n </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> ! </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> Exp </ms> <ms> [ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <apply> <ci> FractionBox </ci> <apply> <ci> ErrorBox </ci> <ms> ∂ </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> ∂ </ms> <ms> z </ms> </list> </apply> </apply> </list> </apply> <ms> z </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ∂ </ms> <ms> . </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> ∂ </ms> <ms> z </ms> </list> </apply> </apply> </list> </apply> <ms> ] </ms> </list> </apply> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> n </ms> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List["Nest", "[", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z"]]], RowBox[List["(", RowBox[List["z", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z"]]], "#1"]]]], ")"]]]]]], "&"]], ",", SuperscriptBox["z", "n"], ",", "k"]], "]"]], RowBox[List["k", "!"]]]]]]], RowBox[List["n", "!"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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