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http://functions.wolfram.com/05.02.23.0001.01
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Sum[(Pochhammer[\[Lambda], n - k] LaguerreL[k, z])/(n - k)!, {k, 0, n}] ==
LaguerreL[n, \[Lambda], z]
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Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["\[Lambda]", ",", RowBox[List["n", "-", "k"]]]], "]"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["k", ",", "z"]], "]"]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["n", "-", "k"]], ")"]], "!"]], " "]]]]], "\[Equal]", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]]]]]]
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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> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mfrac> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mi> λ </mi> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> k </mi> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", "\[Lambda]", ")"]], RowBox[List["n", "-", "k"]]], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <msub> <mi> L </mi> <mi> k </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mfrac> </mrow> <mo> ⩵ </mo> <mrow> <msubsup> <mi> L </mi> <mi> n </mi> <mi> λ </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> Pochhammer </ci> <ci> λ </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <ci> LaguerreL </ci> <ci> k </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <factorial /> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> LaguerreL </ci> <ci> n </ci> <ci> λ </ci> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "n_"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List["\[Lambda]_", ",", RowBox[List["n_", "-", "k_"]]]], "]"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["k_", ",", "z_"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["n_", "-", "k_"]], ")"]], "!"]]]]], "]"]], "\[RuleDelayed]", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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