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ParabolicCylinderD




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ParabolicCylinderD[nu,z] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/07.41.06.0010.01









  


  








Input Form





ParabolicCylinderD[\[Nu], z] == (2^(\[Nu]/2) Sqrt[Pi] ((1/Gamma[(1 - \[Nu])/2]) Hypergeometric1F1[ -(\[Nu]/2), 1/2, z^2/2] - ((Sqrt[2] z)/Gamma[-(\[Nu]/2)]) Hypergeometric1F1[(1 - \[Nu])/2, 3/2, z^2/2]))/E^(z^2/4)








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ParabolicCylinderD", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List["\[Nu]", "/", "2"]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["Hypergeometric1F1", "[", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", FractionBox["1", "2"], ",", FractionBox[SuperscriptBox["z", "2"], "2"]]], "]"]], RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "]"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox["2"], " ", "z"]], ")"]], " ", RowBox[List["Hypergeometric1F1", "[", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], ",", FractionBox["3", "2"], ",", FractionBox[SuperscriptBox["z", "2"], "2"]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["-", FractionBox["\[Nu]", "2"]]], "]"]]]]], ")"]]]]]]]]


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





2007-05-02