Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











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/07.03.03.0019.01









  


  










Input Form





LaguerreL[10, \[Lambda], z] == (1/3628800) (z^10 - 10 z^9 (10 + \[Lambda]) + 45 z^8 (90 + 19 \[Lambda] + \[Lambda]^2) - 120 z^7 (720 + 242 \[Lambda] + 27 \[Lambda]^2 + \[Lambda]^3) + 210 z^6 (5040 + 2414 \[Lambda] + 431 \[Lambda]^2 + 34 \[Lambda]^3 + \[Lambda]^4) - 252 z^5 (30240 + 19524 \[Lambda] + 5000 \[Lambda]^2 + 635 \[Lambda]^3 + 40 \[Lambda]^4 + \[Lambda]^5) + 210 z^4 (151200 + 127860 \[Lambda] + 44524 \[Lambda]^2 + 8175 \[Lambda]^3 + 835 \[Lambda]^4 + 45 \[Lambda]^5 + \[Lambda]^6) - 120 z^3 (604800 + 662640 \[Lambda] + 305956 \[Lambda]^2 + 77224 \[Lambda]^3 + 11515 \[Lambda]^4 + 1015 \[Lambda]^5 + 49 \[Lambda]^6 + \[Lambda]^7) + 45 z^2 (1814400 + 2592720 \[Lambda] + 1580508 \[Lambda]^2 + 537628 \[Lambda]^3 + 111769 \[Lambda]^4 + 14560 \[Lambda]^5 + 1162 \[Lambda]^6 + 52 \[Lambda]^7 + \[Lambda]^8) - 10 z (3628800 + 6999840 \[Lambda] + 5753736 \[Lambda]^2 + 2655764 \[Lambda]^3 + 761166 \[Lambda]^4 + 140889 \[Lambda]^5 + 16884 \[Lambda]^6 + 1266 \[Lambda]^7 + 54 \[Lambda]^8 + \[Lambda]^9) + 3628800 + 10628640 \[Lambda] + 12753576 \[Lambda]^2 + 8409500 \[Lambda]^3 + 3416930 \[Lambda]^4 + 902055 \[Lambda]^5 + 157773 \[Lambda]^6 + 18150 \[Lambda]^7 + 1320 \[Lambda]^8 + 55 \[Lambda]^9 + \[Lambda]^10)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["10", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "3628800"], RowBox[List["(", RowBox[List[SuperscriptBox["z", "10"], "-", RowBox[List["10", " ", SuperscriptBox["z", "9"], " ", RowBox[List["(", RowBox[List["10", "+", "\[Lambda]"]], ")"]]]], "+", RowBox[List["45", " ", SuperscriptBox["z", "8"], " ", RowBox[List["(", RowBox[List["90", "+", RowBox[List["19", " ", "\[Lambda]"]], "+", SuperscriptBox["\[Lambda]", "2"]]], ")"]]]], "-", RowBox[List["120", " ", SuperscriptBox["z", "7"], " ", RowBox[List["(", RowBox[List["720", "+", RowBox[List["242", " ", "\[Lambda]"]], "+", RowBox[List["27", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", SuperscriptBox["\[Lambda]", "3"]]], ")"]]]], "+", RowBox[List["210", " ", SuperscriptBox["z", "6"], " ", RowBox[List["(", RowBox[List["5040", "+", RowBox[List["2414", " ", "\[Lambda]"]], "+", RowBox[List["431", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["34", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", SuperscriptBox["\[Lambda]", "4"]]], ")"]]]], "-", RowBox[List["252", " ", SuperscriptBox["z", "5"], " ", RowBox[List["(", RowBox[List["30240", "+", RowBox[List["19524", " ", "\[Lambda]"]], "+", RowBox[List["5000", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["635", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["40", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", SuperscriptBox["\[Lambda]", "5"]]], ")"]]]], "+", RowBox[List["210", " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["151200", "+", RowBox[List["127860", " ", "\[Lambda]"]], "+", RowBox[List["44524", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["8175", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["835", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["45", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", SuperscriptBox["\[Lambda]", "6"]]], ")"]]]], "-", RowBox[List["120", " ", SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List["604800", "+", RowBox[List["662640", " ", "\[Lambda]"]], "+", RowBox[List["305956", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["77224", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["11515", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["1015", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", RowBox[List["49", " ", SuperscriptBox["\[Lambda]", "6"]]], "+", SuperscriptBox["\[Lambda]", "7"]]], ")"]]]], "+", RowBox[List["45", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["1814400", "+", RowBox[List["2592720", " ", "\[Lambda]"]], "+", RowBox[List["1580508", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["537628", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["111769", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["14560", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", RowBox[List["1162", " ", SuperscriptBox["\[Lambda]", "6"]]], "+", RowBox[List["52", " ", SuperscriptBox["\[Lambda]", "7"]]], "+", SuperscriptBox["\[Lambda]", "8"]]], ")"]]]], "-", RowBox[List["10", " ", "z", " ", RowBox[List["(", RowBox[List["3628800", "+", RowBox[List["6999840", " ", "\[Lambda]"]], "+", RowBox[List["5753736", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["2655764", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["761166", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["140889", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", RowBox[List["16884", " ", SuperscriptBox["\[Lambda]", "6"]]], "+", RowBox[List["1266", " ", SuperscriptBox["\[Lambda]", "7"]]], "+", RowBox[List["54", " ", SuperscriptBox["\[Lambda]", "8"]]], "+", SuperscriptBox["\[Lambda]", "9"]]], ")"]]]], "+", "3628800", "+", RowBox[List["10628640", " ", "\[Lambda]"]], "+", RowBox[List["12753576", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["8409500", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["3416930", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["902055", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", RowBox[List["157773", " ", SuperscriptBox["\[Lambda]", "6"]]], "+", RowBox[List["18150", " ", SuperscriptBox["\[Lambda]", "7"]]], "+", RowBox[List["1320", " ", SuperscriptBox["\[Lambda]", "8"]]], "+", RowBox[List["55", " ", SuperscriptBox["\[Lambda]", "9"]]], "+", SuperscriptBox["\[Lambda]", "10"]]], ")"]]]]]]]]










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> 10 </mn> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3628800 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 10 </mn> </msup> <mo> - </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 10 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 45 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 19 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 90 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 120 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> <mo> + </mo> <mrow> <mn> 27 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 242 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 720 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 210 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> <mo> + </mo> <mrow> <mn> 34 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 431 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2414 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 5040 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 252 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 5 </mn> </msup> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 635 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5000 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 19524 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 30240 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 210 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 6 </mn> </msup> <mo> + </mo> <mrow> <mn> 45 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 835 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8175 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 44524 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 127860 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 151200 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 120 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 7 </mn> </msup> <mo> + </mo> <mrow> <mn> 49 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1015 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11515 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 77224 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 305956 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 662640 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 604800 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 45 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 8 </mn> </msup> <mo> + </mo> <mrow> <mn> 52 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1162 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 14560 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 111769 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 537628 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1580508 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2592720 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 1814400 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 9 </mn> </msup> <mo> + </mo> <mrow> <mn> 54 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1266 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16884 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 140889 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 761166 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2655764 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5753736 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6999840 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 3628800 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <msup> <mi> &#955; </mi> <mn> 10 </mn> </msup> <mo> + </mo> <mrow> <mn> 55 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1320 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 18150 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 157773 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 902055 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3416930 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8409500 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12753576 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10628640 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 3628800 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <cn type='integer'> 10 </cn> <ci> &#955; </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 3628800 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 10 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 45 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 19 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 90 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 120 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 27 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 242 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 720 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 210 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 34 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 431 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2414 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 5040 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 252 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 635 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5000 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19524 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 30240 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 210 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 6 </cn> </apply> <apply> <times /> <cn type='integer'> 45 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 835 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8175 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 44524 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 127860 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 151200 </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'> 120 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 7 </cn> </apply> <apply> <times /> <cn type='integer'> 49 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1015 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11515 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 77224 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 305956 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 662640 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 604800 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 45 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> 52 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1162 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 14560 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 111769 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 537628 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1580508 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2592720 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 1814400 </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'> 10 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 9 </cn> </apply> <apply> <times /> <cn type='integer'> 54 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1266 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16884 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 140889 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 761166 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2655764 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5753736 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6999840 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 3628800 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 10 </cn> </apply> <apply> <times /> <cn type='integer'> 55 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1320 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 18150 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 157773 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 902055 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3416930 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8409500 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12753576 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10628640 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 3628800 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["10", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["z", "10"], "-", RowBox[List["10", " ", SuperscriptBox["z", "9"], " ", RowBox[List["(", RowBox[List["10", "+", "\[Lambda]"]], ")"]]]], "+", RowBox[List["45", " ", SuperscriptBox["z", "8"], " ", RowBox[List["(", RowBox[List["90", "+", RowBox[List["19", " ", "\[Lambda]"]], "+", SuperscriptBox["\[Lambda]", "2"]]], ")"]]]], "-", RowBox[List["120", " ", SuperscriptBox["z", "7"], " ", RowBox[List["(", RowBox[List["720", "+", RowBox[List["242", " ", "\[Lambda]"]], "+", RowBox[List["27", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", SuperscriptBox["\[Lambda]", "3"]]], ")"]]]], "+", RowBox[List["210", " ", SuperscriptBox["z", "6"], " ", RowBox[List["(", RowBox[List["5040", "+", RowBox[List["2414", " ", "\[Lambda]"]], "+", RowBox[List["431", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["34", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", SuperscriptBox["\[Lambda]", "4"]]], ")"]]]], "-", RowBox[List["252", " ", SuperscriptBox["z", "5"], " ", RowBox[List["(", RowBox[List["30240", "+", RowBox[List["19524", " ", "\[Lambda]"]], "+", RowBox[List["5000", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["635", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["40", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", SuperscriptBox["\[Lambda]", "5"]]], ")"]]]], "+", RowBox[List["210", " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["151200", "+", RowBox[List["127860", " ", "\[Lambda]"]], "+", RowBox[List["44524", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["8175", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["835", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["45", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", SuperscriptBox["\[Lambda]", "6"]]], ")"]]]], "-", RowBox[List["120", " ", SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List["604800", "+", RowBox[List["662640", " ", "\[Lambda]"]], "+", RowBox[List["305956", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["77224", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["11515", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["1015", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", RowBox[List["49", " ", SuperscriptBox["\[Lambda]", "6"]]], "+", SuperscriptBox["\[Lambda]", "7"]]], ")"]]]], "+", RowBox[List["45", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["1814400", "+", RowBox[List["2592720", " ", "\[Lambda]"]], "+", RowBox[List["1580508", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["537628", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["111769", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["14560", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", RowBox[List["1162", " ", SuperscriptBox["\[Lambda]", "6"]]], "+", RowBox[List["52", " ", SuperscriptBox["\[Lambda]", "7"]]], "+", SuperscriptBox["\[Lambda]", "8"]]], ")"]]]], "-", RowBox[List["10", " ", "z", " ", RowBox[List["(", RowBox[List["3628800", "+", RowBox[List["6999840", " ", "\[Lambda]"]], "+", RowBox[List["5753736", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["2655764", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["761166", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["140889", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", RowBox[List["16884", " ", SuperscriptBox["\[Lambda]", "6"]]], "+", RowBox[List["1266", " ", SuperscriptBox["\[Lambda]", "7"]]], "+", RowBox[List["54", " ", SuperscriptBox["\[Lambda]", "8"]]], "+", SuperscriptBox["\[Lambda]", "9"]]], ")"]]]], "+", "3628800", "+", RowBox[List["10628640", " ", "\[Lambda]"]], "+", RowBox[List["12753576", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["8409500", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["3416930", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["902055", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", RowBox[List["157773", " ", SuperscriptBox["\[Lambda]", "6"]]], "+", RowBox[List["18150", " ", SuperscriptBox["\[Lambda]", "7"]]], "+", RowBox[List["1320", " ", SuperscriptBox["\[Lambda]", "8"]]], "+", RowBox[List["55", " ", SuperscriptBox["\[Lambda]", "9"]]], "+", SuperscriptBox["\[Lambda]", "10"]]], "3628800"]]]]]










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





2001-10-29





© 1998-2014 Wolfram Research, Inc.