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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LaguerreL[nu,z] > Identities > Functional identities > Relations of special kind





http://functions.wolfram.com/07.02.17.0006.01









  


  








Input Form





LaguerreL[\[Nu], z] == (1/z) (\[Nu] LaguerreL[\[Nu], -1, z] - (\[Nu] + 1) LaguerreL[\[Nu] + 1, -1, z])








Standard Form





Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "z"], RowBox[List["(", RowBox[List[RowBox[List["\[Nu]", " ", RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]", ",", RowBox[List["-", "1"]], ",", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "+", "1"]], ")"]], " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", RowBox[List["-", "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> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mi> &#957; </mi> <mo> &#8290; </mo> <mrow> <msubsup> <mi> L </mi> <mi> &#957; </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msubsup> <mi> L </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mi> z </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> &#957; </ci> <apply> <ci> LaguerreL </ci> <ci> &#957; </ci> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> LaguerreL </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2001-10-29