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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,z] > Specific values > Specialized values > For fixed z





http://functions.wolfram.com/05.02.03.0005.01









  


  








Input Form





LaguerreL[3, z] == (1/6) (6 - 18 z + 9 z^2 - z^3)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["3", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["6", "-", RowBox[List["18", " ", "z"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]], "-", SuperscriptBox["z", "3"]]], ")"]]]]]]]]








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> <mn> 3 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> - </mo> <mrow> <mn> 18 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <plus /> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List["6", "-", RowBox[List["18", " ", "z"]], "+", RowBox[List["9", " ", SuperscriptBox["z", "2"]]], "-", SuperscriptBox["z", "3"]]], ")"]]]]]]]]


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





2001-10-29