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 LaguerreL

 http://functions.wolfram.com/05.08.06.0005.01

 Input Form

 LaguerreL[n, \[Lambda], z] == Sum[((-1)^k Binomial[n + \[Lambda], n - k] z^k)/ k!, {k, 0, n}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n", "+", "\[Lambda]"]], ",", RowBox[List["n", "-", "k"]]]], "]"]], " ", SuperscriptBox["z", "k"]]], RowBox[List["k", "!"]]]]]]]]]

 MathML Form

 L n λ ( z ) k = 0 n ( - 1 ) k k ! ( n + λ n - k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["n", "+", "\[Lambda]"]], Identity, Rule[Editable, True]]], List[TagBox[RowBox[List["n", "-", "k"]], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] z k LaguerreL n λ z k 0 n -1 k k -1 Binomial n λ n -1 k z k [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n", "+", "\[Lambda]"]], ",", RowBox[List["n", "-", "k"]]]], "]"]], " ", SuperscriptBox["z", "k"]]], RowBox[List["k", "!"]]]]]]]]]

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

 2001-10-29