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 HermiteH

 http://functions.wolfram.com/05.01.26.0005.01

 Input Form

 HermiteH[n, z] == 2^n z HypergeometricU[(1 - n)/2, 3/2, z^2] /; Re[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["2", "n"], "z", " ", RowBox[List["HypergeometricU", "[", RowBox[List[FractionBox[RowBox[List["1", "-", "n"]], "2"], ",", FractionBox["3", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]

 MathML Form

 H n ( z ) 2 n z U TagBox["U", HypergeometricU] ( 1 - n 2 , 3 2 , z 2 ) /; Re ( z ) > 0 Condition HermiteH n z 2 n z HypergeometricU 1 -1 n 2 -1 3 2 z 2 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HermiteH", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", "n"], " ", "z", " ", RowBox[List["HypergeometricU", "[", RowBox[List[FractionBox[RowBox[List["1", "-", "n"]], "2"], ",", FractionBox["3", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]

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

 2001-10-29