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 LaguerreL

 http://functions.wolfram.com/05.08.03.0003.01

 Input Form

 LaguerreL[n, -(1/2), z] == ((-1)^n/(2^(2 n) n!)) HermiteH[2 n, Sqrt[z]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List["-", FractionBox["1", "2"]]], ",", " ", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["2", " ", "n"]]], " ", RowBox[List["n", "!"]]]]], RowBox[List["HermiteH", "[", RowBox[List[RowBox[List["2", "n"]], ",", SqrtBox["z"]]], "]"]]]]]]]]

 MathML Form

 L n - 1 2 ( z ) ( - 1 ) n 2 2 n n ! H 2 n ( z ) LaguerreL n -1 1 2 z -1 n 2 2 n n -1 HermiteH 2 n z 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["HermiteH", "[", RowBox[List[RowBox[List["2", " ", "n"]], ",", SqrtBox["z"]]], "]"]]]], RowBox[List[SuperscriptBox["2", RowBox[List["2", " ", "n"]]], " ", RowBox[List["n", "!"]]]]]]]]]

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

 2001-10-29