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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/05.02.06.0016.01









  


  








Input Form





LaguerreL[n, z] == HypergeometricPFQRegularized[{{-n}, {}, {}}, {{1}, {}, {}}, Subscript[z, 0], z - Subscript[z, 0]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["-", "n"]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", SubscriptBox["z", "0"], ",", RowBox[List["z", "-", SubscriptBox["z", "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> <msub> <mi> L </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msubsup> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mrow> <mn> 1 </mn> <mo> &#8290; </mo> <mn> 0 </mn> <mo> &#8290; </mo> <mn> 0 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> &#8290; </mo> <mn> 0 </mn> <mo> &#8290; </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> ( </mo> <mrow> <mrow> <mtable> <mtr> <mtd> <mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> ; </mo> </mrow> <mo> ; </mo> </mrow> <mo> ; </mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mrow> <mn> 1 </mn> <mo> ; </mo> </mrow> <mo> ; </mo> </mrow> <mo> ; </mo> </mrow> </mtd> </mtr> </mtable> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <ci> n </ci> <ci> z </ci> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> OverTilde </ci> <ci> F </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <list> <list> <apply> <ci> CompoundExpression </ci> <apply> <ci> CompoundExpression </ci> <apply> <ci> CompoundExpression </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <ci> Null </ci> </apply> <ci> Null </ci> </apply> <ci> Null </ci> </apply> </list> <list> <apply> <ci> CompoundExpression </ci> <apply> <ci> CompoundExpression </ci> <apply> <ci> CompoundExpression </ci> <cn type='integer'> 1 </cn> <ci> Null </ci> </apply> <ci> Null </ci> </apply> <ci> Null </ci> </apply> </list> </list> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["-", "n"]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", SubscriptBox["zz", "0"], ",", RowBox[List["z", "-", SubscriptBox["zz", "0"]]]]], "]"]]]]]]


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





2007-05-02