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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,lambda,z] > Identities > Recurrence identities > Consecutive neighbors > With respect to lambda





http://functions.wolfram.com/05.08.17.0010.01









  


  








Input Form





LaguerreL[n, \[Lambda], z] == ((1 + z + \[Lambda])/(1 + \[Lambda] + n)) LaguerreL[n, 1 + \[Lambda], z] - (z/(\[Lambda] + n + 1)) LaguerreL[n, 2 + \[Lambda], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox[RowBox[List["1", "+", "z", "+", "\[Lambda]"]], RowBox[List["1", "+", "\[Lambda]", "+", "n"]]], " ", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List["1", "+", "\[Lambda]"]], ",", "z"]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["z", " "]], RowBox[List["\[Lambda]", "+", "n", "+", "1"]]], RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List["2", "+", "\[Lambda]"]], ",", "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> <msubsup> <mi> L </mi> <mi> n </mi> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mrow> <mi> z </mi> <mo> + </mo> <mi> &#955; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mi> &#955; </mi> <mo> + </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <mi> L </mi> <mi> n </mi> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mi> z </mi> <mtext> </mtext> </mrow> <mrow> <mi> &#955; </mi> <mo> + </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <mi> L </mi> <mi> n </mi> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <ci> n </ci> <ci> &#955; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> z </ci> <ci> &#955; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> &#955; </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> LaguerreL </ci> <ci> n </ci> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <ci> &#955; </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> LaguerreL </ci> <ci> n </ci> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "z", "+", "\[Lambda]"]], ")"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List["1", "+", "\[Lambda]"]], ",", "z"]], "]"]]]], RowBox[List["1", "+", "\[Lambda]", "+", "n"]]], "-", FractionBox[RowBox[List["z", " ", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List["2", "+", "\[Lambda]"]], ",", "z"]], "]"]]]], RowBox[List["\[Lambda]", "+", "n", "+", "1"]]]]]]]]]


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





2007-05-02