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AiryAi






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryAi[z] > Differentiation > Fractional integro-differentiation





http://functions.wolfram.com/03.05.20.0004.01









  


  










Input Form





D[AiryAi[z], {z, \[Alpha]}] == (3^(\[Alpha] - 4/3) (3^(2/3) Gamma[1/3] HypergeometricPFQRegularized[ {1/3, 1}, {(1 - \[Alpha])/3, (2 - \[Alpha])/3, 1 - \[Alpha]/3}, z^3/9] - z Gamma[2/3] HypergeometricPFQRegularized[{2/3, 1}, {(2 - \[Alpha])/3, 1 - \[Alpha]/3, (4 - \[Alpha])/3}, z^3/9]))/ z^\[Alpha]










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["AiryAi", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["3", RowBox[List["\[Alpha]", "-", FractionBox["4", "3"]]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "3"], ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Alpha]"]], "3"], ",", FractionBox[RowBox[List["2", "-", "\[Alpha]"]], "3"], ",", RowBox[List["1", "-", FractionBox["\[Alpha]", "3"]]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "3"], "9"]]], "]"]]]], "-", RowBox[List["z", " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["2", "3"], ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["2", "-", "\[Alpha]"]], "3"], ",", RowBox[List["1", "-", FractionBox["\[Alpha]", "3"]]], ",", FractionBox[RowBox[List["4", "-", "\[Alpha]"]], "3"]]], "}"]], ",", FractionBox[SuperscriptBox["z", "3"], "9"]]], "]"]]]]]], ")"]]]]]]]]










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





2001-10-29





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