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variants of this functions
HermiteH






Mathematica Notation

Traditional Notation









Polynomials > HermiteH[n,z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/05.01.06.0012.01









  


  










Input Form





HermiteH[n, z] == Sum[(1/k!) (((2^(k + n) Pi)/(Subscript[z, 0]^k Gamma[(1 - n)/2])) HypergeometricPFQRegularized[{1, -(n/2)}, {(1 - k)/2, 1 - k/2}, Subscript[z, 0]^2] - ((2^(k + n) Pi Subscript[z, 0]^(1 - k))/ Gamma[-(n/2)]) HypergeometricPFQRegularized[{1, (1 - n)/2}, {1 - k/2, (3 - k)/2}, Subscript[z, 0]^2]) (z - Subscript[z, 0])^k, {k, 0, n}]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HermiteH", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["k", "+", "n"]]], " ", "\[Pi]", " ", SubsuperscriptBox["zz", "0", RowBox[List["-", "k"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["-", FractionBox["n", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "k"]], "2"], ",", RowBox[List["1", "-", FractionBox["k", "2"]]]]], "}"]], ",", SubsuperscriptBox["zz", "0", "2"]]], "]"]]]], RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "-", "n"]], "2"], "]"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["k", "+", "n"]]], " ", "\[Pi]", " ", SubsuperscriptBox["zz", "0", RowBox[List["1", "-", "k"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox[RowBox[List["1", "-", "n"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["k", "2"]]], ",", FractionBox[RowBox[List["3", "-", "k"]], "2"]]], "}"]], ",", SubsuperscriptBox["zz", "0", "2"]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["-", FractionBox["n", "2"]]], "]"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]]]]










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





2007-05-02





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