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 HermiteH

 http://functions.wolfram.com/05.01.21.0017.01

 Input Form

 Integrate[HermiteH[n, t]/E^(z - t)^2, {t, -Infinity, Infinity}] == 2^n Sqrt[Pi] z^n

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", RowBox[List["-", "\[Infinity]"]], "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "t"]], ")"]], "2"]]]], " ", RowBox[List["HermiteH", "[", RowBox[List["n", ",", "t"]], "]"]]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[SuperscriptBox["2", "n"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", "n"]]]]]]]

 MathML Form

 - - ( z - t ) 2 H n ( t ) t 2 n π z n t -1 -1 z -1 t 2 HermiteH n t 2 n 1 2 z n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", RowBox[List["-", "\[Infinity]"]], "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["z_", "-", "t_"]], ")"]], "2"]]]], " ", RowBox[List["HermiteH", "[", RowBox[List["n_", ",", "t_"]], "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", "n"], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", "n"]]]]]]]

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

 2001-10-29