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http://functions.wolfram.com/05.02.11.0001.01
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LaguerreL[n, z] == SeriesTerm[Exp[(t z)/(t - 1)]/(1 - t), {t, 0, n}]
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Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List["SeriesTerm", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "t"]], ")"]], RowBox[List["-", "1"]]], " ", RowBox[List["Exp", "[", FractionBox[RowBox[List["t", " ", "z"]], RowBox[List["t", "-", "1"]]], "]"]]]], ",", RowBox[List["{", RowBox[List["t", ",", "0", ",", "n"]], "}"]]]], "]"]]]]]]
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<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> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <msup> <mi> t </mi> <mi> n </mi> </msup> <mtext> </mtext> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> t </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> t </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mrow> <mi> t </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <mi> L </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <msup> <mi> t </mi> <mi> n </mi> </msup> <mtext> </mtext> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> t </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> t </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mrow> <mi> t </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["SeriesTerm", "[", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["t", " ", "z"]], RowBox[List["t", "-", "1"]]]], RowBox[List["1", "-", "t"]]], ",", RowBox[List["{", RowBox[List["t", ",", "0", ",", "n"]], "}"]]]], "]"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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