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ParabolicCylinderD






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ParabolicCylinderD[nu,z] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/07.41.20.0028.01









  


  










Input Form





D[E^(z^2/4) ParabolicCylinderD[\[Nu], z], {z, \[Alpha]}] == ((2^(\[Alpha] + \[Nu]/2) Pi)/(z^\[Alpha] Gamma[(1 - \[Nu])/2])) HypergeometricPFQRegularized[{1, -(\[Nu]/2)}, {(1 - \[Alpha])/2, 1 - \[Alpha]/2}, z^2/2] - ((2^((\[Nu] - 1)/2 + \[Alpha]) Pi z^(1 - \[Alpha]))/Gamma[-(\[Nu]/2)]) HypergeometricPFQRegularized[{1, (1 - \[Nu])/2}, {1 - \[Alpha]/2, (3 - \[Alpha])/2}, z^2/2]










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["z_", "2"], "4"]], " ", RowBox[List["ParabolicCylinderD", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], ")"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "+", FractionBox["\[Nu]", "2"]]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Alpha]"]], "2"], ",", RowBox[List["1", "-", FractionBox["\[Alpha]", "2"]]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "2"], "2"]]], "]"]]]], RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "]"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "1"]], "2"], "+", "\[Alpha]"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["\[Alpha]", "2"]]], ",", FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "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





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