LaguerreL[8, z] == (1/40320) (40320 - 322560 z + 564480 z^2 - 376320 z^3 + 117600 z^4 - 18816 z^5 + 1568 z^6 - 64 z^7 + z^8)

Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["8", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "40320"], RowBox[List["(", RowBox[List["40320", "-", RowBox[List["322560", " ", "z"]], "+", RowBox[List["564480", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["376320", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["117600", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["18816", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1568", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["64", " ", SuperscriptBox["z", "7"]]], "+", SuperscriptBox["z", "8"]]], ")"]]]]]]]]

<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> <mn> 8 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 40320 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 40320 </mn> <mo> - </mo> <mrow> <mn> 322560 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 564480 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 376320 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 117600 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 18816 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1568 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 40320 </cn> <apply> <plus /> <cn type='integer'> 40320 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 322560 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 564480 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 376320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 117600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18816 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1568 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["8", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["40320", "-", RowBox[List["322560", " ", "z"]], "+", RowBox[List["564480", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["376320", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["117600", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["18816", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1568", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["64", " ", SuperscriptBox["z", "7"]]], "+", SuperscriptBox["z", "8"]]], "40320"]]]]]

2001-10-29