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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,lambda,z] > Summation > Finite summation





http://functions.wolfram.com/05.08.23.0005.01









  


  








Input Form





Sum[LaguerreL[k, \[Mu], Subscript[z, 1]] LaguerreL[n - k, \[Lambda], Subscript[z, 2]], {k, 0, n}] == LaguerreL[n, \[Lambda] + \[Mu] + 1, Subscript[z, 1] + Subscript[z, 2]]








Standard Form





Cell[BoxData[RowBox[List[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"]], ",", "\[Lambda]", ",", SubscriptBox["z", "2"]]], "]"]]]]]], "\[Equal]", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List["\[Lambda]", "+", "\[Mu]", "+", "1"]], ",", RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]]]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munderover> <mo> &#8721; </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> &#956; </mi> </msubsup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msubsup> <mi> L </mi> <mrow> <mi> n </mi> <mo> - </mo> <mi> k </mi> </mrow> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <msubsup> <mi> L </mi> <mi> n </mi> <mrow> <mi> &#955; </mi> <mo> + </mo> <mi> &#956; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msubsup> <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> </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> LaguerreL </ci> <ci> k </ci> <ci> &#956; </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> <ci> &#955; </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> LaguerreL </ci> <ci> n </ci> <apply> <plus /> <ci> &#955; </ci> <ci> &#956; </ci> <cn type='integer'> 1 </cn> </apply> <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> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", 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_"]], ",", "\[Lambda]_", ",", SubscriptBox["z_", "2"]]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List["\[Lambda]", "+", "\[Mu]", "+", "1"]], ",", RowBox[List[SubscriptBox["zz", "1"], "+", SubscriptBox["zz", "2"]]]]], "]"]]]]]]


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





2001-10-29