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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/07.03.03.0014.01









  


  










Input Form





LaguerreL[5, \[Lambda], z] == (1/120) (-z^5 + 5 z^4 (5 + \[Lambda]) - 10 z^3 (20 + 9 \[Lambda] + \[Lambda]^2) + 10 z^2 (60 + 47 \[Lambda] + 12 \[Lambda]^2 + \[Lambda]^3) - 5 z (120 + 154 \[Lambda] + 71 \[Lambda]^2 + 14 \[Lambda]^3 + \[Lambda]^4) + 120 + 274 \[Lambda] + 225 \[Lambda]^2 + 85 \[Lambda]^3 + 15 \[Lambda]^4 + \[Lambda]^5)










Standard Form





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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> 5 </mn> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 120 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 20 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 47 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 60 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> <mo> + </mo> <mrow> <mn> 14 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 71 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 154 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 120 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <msup> <mi> &#955; </mi> <mn> 5 </mn> </msup> <mo> + </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 85 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 225 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 274 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 120 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <cn type='integer'> 5 </cn> <ci> &#955; </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 120 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 20 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 47 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 60 </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'> 5 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 14 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 71 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 154 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 120 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 85 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 225 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 274 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 120 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["5", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "120"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "5"]]], "+", RowBox[List["5", " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["5", "+", "\[Lambda]"]], ")"]]]], "-", RowBox[List["10", " ", SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List["20", "+", RowBox[List["9", " ", "\[Lambda]"]], "+", SuperscriptBox["\[Lambda]", "2"]]], ")"]]]], "+", RowBox[List["10", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["60", "+", RowBox[List["47", " ", "\[Lambda]"]], "+", RowBox[List["12", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", SuperscriptBox["\[Lambda]", "3"]]], ")"]]]], "-", RowBox[List["5", " ", "z", " ", RowBox[List["(", RowBox[List["120", "+", RowBox[List["154", " ", "\[Lambda]"]], "+", RowBox[List["71", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["14", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", SuperscriptBox["\[Lambda]", "4"]]], ")"]]]], "+", "120", "+", RowBox[List["274", " ", "\[Lambda]"]], "+", RowBox[List["225", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["85", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["15", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", SuperscriptBox["\[Lambda]", "5"]]], ")"]]]]]]]]










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





2001-10-29





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