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http://functions.wolfram.com/05.08.16.0001.01
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LaguerreL[n, \[Lambda], -z] ==
((-1)^\[Lambda] LaguerreL[-\[Lambda] - n - 1, \[Lambda], z])/E^z /;
Element[\[Lambda], Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "\[Lambda]", ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "\[Lambda]"], " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[Lambda]"]], "-", "n", "-", "1"]], ",", "\[Lambda]", ",", "z"]], "]"]]]]]], "/;", RowBox[List["Element", "[", RowBox[List["\[Lambda]", ",", "Integers"]], "]"]]]]]]
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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> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> λ </mi> </msup> <mo> ⁢ </mo> <mrow> <msubsup> <mi> L </mi> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mi> λ </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> λ </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> λ </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> LaguerreL </ci> <ci> n </ci> <ci> λ </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> -1 </cn> <ci> λ </ci> </apply> <apply> <ci> LaguerreL </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> λ </ci> </apply> <cn type='integer'> -1 </cn> </apply> <ci> λ </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <in /> <ci> λ </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "\[Lambda]"], " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[Lambda]"]], "-", "n", "-", "1"]], ",", "\[Lambda]", ",", "z"]], "]"]]]], "/;", RowBox[List["\[Lambda]", "\[Element]", "Integers"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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