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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/05.08.03.0007.01









  


  








Input Form





LaguerreL[n, \[Lambda], z] == Nest[-D[#1, z] & , LaguerreL[n + \[Lambda], z], \[Lambda]] /; Element[\[Lambda], Integers] && \[Lambda] > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Equal]", RowBox[List["Nest", "[", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["D", "[", RowBox[List["#", ",", "z"]], "]"]]]], "&"]], ",", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["n", "+", "\[Lambda]"]], ",", "z"]], "]"]], ",", "\[Lambda]"]], "]"]]]], "/;", RowBox[List[RowBox[List["\[Lambda]", "\[Element]", "Integers"]], "\[And]", RowBox[List["\[Lambda]", ">", "0"]]]]]]]]








MathML Form







<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> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mo> . </mo> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> &#955; </mi> </msup> <mo> &#8290; </mo> <mrow> <msub> <mi> L </mi> <mrow> <mi> n </mi> <mo> + </mo> <mi> &#955; </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#955; </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msubsup> <mi> L </mi> <mi> n </mi> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mo> . </mo> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> &#955; </mi> </msup> <mo> &#8290; </mo> <mrow> <msub> <mi> L </mi> <mrow> <mi> n </mi> <mo> + </mo> <mi> &#955; </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#955; </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Nest", "[", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z"]]], "#1"]]]], "&"]], ",", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["n", "+", "\[Lambda]"]], ",", "z"]], "]"]], ",", "\[Lambda]"]], "]"]], "/;", RowBox[List[RowBox[List["\[Lambda]", "\[Element]", "Integers"]], "&&", RowBox[List["\[Lambda]", ">", "0"]]]]]]]]]]


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





2001-10-29