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 HermiteH

 http://functions.wolfram.com/05.01.06.0007.01

 Input Form

 HermiteH[n, z] == 2^n z^n HypergeometricPFQ[{-(n/2), (1 - n)/2}, {}, -(1/z^2)]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["2", "n"], " ", SuperscriptBox["z", "n"], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], ",", FractionBox[RowBox[List["1", "-", "n"]], "2"]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]], "]"]]]]]]]]

 MathML Form

 H n ( z ) 2 n z n 2 F 0 ( - n 2 , 1 - n 2 ; ; - 1 z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["0", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["1", "-", "n"]], "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] Proportional HermiteH n z 2 n z n HypergeometricPFQ -1 n 2 -1 1 -1 n 2 -1 -1 1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HermiteH", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", "n"], " ", SuperscriptBox["z", "n"], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], ",", FractionBox[RowBox[List["1", "-", "n"]], "2"]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]], "]"]]]]]]]]

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

 2001-10-29