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http://functions.wolfram.com/05.02.16.0002.01
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LaguerreL[n, Subscript[z, 1] + Subscript[z, 2]] ==
Sum[LaguerreL[k, \[Mu], Subscript[z, 1]] LaguerreL[n - k, -\[Mu] - 1,
Subscript[z, 2]], {k, 0, n}]
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Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]]]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["k", ",", "\[Mu]", ",", SubscriptBox["z", "1"]]], "]"]], RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["n", "-", "k"]], ",", RowBox[List[RowBox[List["-", "\[Mu]"]], "-", "1"]], ",", SubscriptBox["z", "2"]]], "]"]]]]]]]]]]
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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> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mrow> <msubsup> <mi> L </mi> <mi> k </mi> <mi> μ </mi> </msubsup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <mi> L </mi> <mrow> <mi> n </mi> <mo> - </mo> <mi> k </mi> </mrow> <mrow> <mrow> <mo> - </mo> <mi> μ </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <ci> n </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> LaguerreL </ci> <ci> k </ci> <ci> μ </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> LaguerreL </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> μ </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", RowBox[List[SubscriptBox["z_", "1"], "+", SubscriptBox["z_", "2"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["k", ",", "\[Mu]", ",", SubscriptBox["zz", "1"]]], "]"]], " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["n", "-", "k"]], ",", RowBox[List[RowBox[List["-", "\[Mu]"]], "-", "1"]], ",", SubscriptBox["zz", "2"]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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