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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LaguerreL[nu,lambda,z] > Specific values > Specialized values > For fixed lambda, z





http://functions.wolfram.com/07.03.03.0011.01









  


  








Input Form





LaguerreL[2, \[Lambda], z] == (1/2) (z^2 - 2 z (2 + \[Lambda]) + 3 \[Lambda] + \[Lambda]^2 + 2)








Standard Form





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








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> <mn> 2 </mn> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <mi> &#955; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <cn type='integer'> 2 </cn> <ci> &#955; </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> &#955; </ci> </apply> </apply> </apply> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2001-10-29