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http://functions.wolfram.com/07.03.17.0007.01
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LaguerreL[\[Nu], \[Lambda], z] ==
(1/z) ((\[Nu] + \[Lambda]) LaguerreL[\[Nu], \[Lambda] - 1, z] -
(\[Nu] + 1) LaguerreL[\[Nu] + 1, \[Lambda] - 1, z])
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Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "z"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "+", "\[Lambda]"]], ")"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]", ",", RowBox[List["\[Lambda]", "-", "1"]], ",", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "+", "1"]], ")"]], " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", RowBox[List["\[Lambda]", "-", "1"]], ",", "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> ν </mi> <mi> λ </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mi> λ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <mi> L </mi> <mi> ν </mi> <mrow> <mi> λ </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <mi> L </mi> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mi> λ </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <ci> ν </ci> <ci> λ </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> ν </ci> <ci> λ </ci> </apply> <apply> <ci> LaguerreL </ci> <ci> ν </ci> <apply> <plus /> <ci> λ </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> LaguerreL </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> λ </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]_", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "+", "\[Lambda]"]], ")"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]", ",", RowBox[List["\[Lambda]", "-", "1"]], ",", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "+", "1"]], ")"]], " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", RowBox[List["\[Lambda]", "-", "1"]], ",", "z"]], "]"]]]]]], "z"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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