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http://functions.wolfram.com/05.08.03.0005.01
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LaguerreL[n, 1, z] == (1/z) (n LaguerreL[n - 1, z] - (n - z) LaguerreL[n, z])
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Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "1", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "z"], RowBox[List["(", RowBox[List[RowBox[List["n", " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["n", "-", "z"]], ")"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "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> <msubsup> <mi> L </mi> <mi> n </mi> <mn> 1 </mn> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mi> n </mi> <mo> ⁢ </mo> <mrow> <msub> <mi> L </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> L </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mi> z </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <ci> n </ci> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> n </ci> <apply> <ci> LaguerreL </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <ci> LaguerreL </ci> <ci> n </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "1", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["n", " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["n", "-", "z"]], ")"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "z"]], "]"]]]]]], "z"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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