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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/05.02.16.0001.01









  


  








Input Form





LaguerreL[n, -z] == LaguerreL[-n - 1, z]/E^z








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List[RowBox[List["-", "n"]], "-", "1"]], ",", "z"]], "]"]]]]]]]]








MathML Form







<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> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mtext> </mtext> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msub> <mi> L </mi> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <ci> n </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> <ci> LaguerreL </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List[RowBox[List["-", "n"]], "-", "1"]], ",", "z"]], "]"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29