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 HermiteH

 http://functions.wolfram.com/05.01.20.0004.01

 Input Form

 D[HermiteH[n, z]/E^z^2, z] == (-E^(-z^2)) HermiteH[n + 1, z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["z", "2"]]]], RowBox[List["HermiteH", "[", RowBox[List["n", ",", "z"]], "]"]]]], ")"]]]], "\[Equal]", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["z", "2"]]]]]], RowBox[List["HermiteH", "[", RowBox[List[RowBox[List["n", "+", "1"]], ",", "z"]], "]"]]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["z_", "2"]]]], " ", RowBox[List["HermiteH", "[", RowBox[List["n_", ",", "z_"]], "]"]]]], ")"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["z", "2"]]]]]], " ", RowBox[List["HermiteH", "[", RowBox[List[RowBox[List["n", "+", "1"]], ",", "z"]], "]"]]]]]]]]

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

 2001-10-29