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variants of this functions
HermiteH






Mathematica Notation

Traditional Notation









Polynomials > HermiteH[n,z] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/05.01.20.0007.01









  


  










Input Form





D[HermiteH[n, z], {z, \[Alpha]}] == ((2^(\[Alpha] + n) Pi)/(z^\[Alpha] Gamma[(1 - n)/2])) HypergeometricPFQRegularized[{1, -(n/2)}, {(1 - \[Alpha])/2, 1 - \[Alpha]/2}, z^2] - ((2^(\[Alpha] + n) Pi z^(1 - \[Alpha]))/ Gamma[-(n/2)]) HypergeometricPFQRegularized[{1, (1 - n)/2}, {1 - \[Alpha]/2, (3 - \[Alpha])/2}, z^2]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["HermiteH", "[", RowBox[List["n_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "+", "n"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["-", FractionBox["n", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Alpha]"]], "2"], ",", RowBox[List["1", "-", FractionBox["\[Alpha]", "2"]]]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]], RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "-", "n"]], "2"], "]"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "+", "n"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox[RowBox[List["1", "-", "n"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["\[Alpha]", "2"]]], ",", FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "2"]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["-", FractionBox["n", "2"]]], "]"]]]]]]]]]










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





2001-10-29





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