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 HermiteH

 http://functions.wolfram.com/05.01.27.0003.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29