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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/05.08.03.0012.01









  


  








Input Form





LaguerreL[3, \[Lambda], z] == (1/6) (-z^3 + 3 (3 + \[Lambda]) z^2 - 3 (6 + 5 \[Lambda] + \[Lambda]^2) z + \[Lambda]^3 + 6 \[Lambda]^2 + 11 \[Lambda] + 6)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["3", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "3"]]], "+", " ", RowBox[List["3", RowBox[List["(", RowBox[List["3", "+", "\[Lambda]"]], ")"]], SuperscriptBox["z", "2"]]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["5", " ", "\[Lambda]"]], "+", SuperscriptBox["\[Lambda]", "2"]]], ")"]], "z"]], "+", SuperscriptBox["\[Lambda]", "3"], "+", RowBox[List["6", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["11", " ", "\[Lambda]"]], "+", "6"]], ")"]]]]]]]]








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> 3 </mn> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <cn type='integer'> 3 </cn> <ci> &#955; </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 6 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["3", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "6"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "3"]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List["3", "+", "\[Lambda]"]], ")"]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["5", " ", "\[Lambda]"]], "+", SuperscriptBox["\[Lambda]", "2"]]], ")"]], " ", "z"]], "+", SuperscriptBox["\[Lambda]", "3"], "+", RowBox[List["6", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["11", " ", "\[Lambda]"]], "+", "6"]], ")"]]]]]]]]


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





2001-10-29