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 AiryAi

 http://functions.wolfram.com/03.05.21.0015.01

 Input Form

 Integrate[(Sqrt[z] AiryAi[a z])/E^((2/3) (a z)^(3/2)), z] == (1/(15 a^2 Sqrt[z] Gamma[2/3])) ((2 (3 a^2 z^2 AiryAi[a z] Gamma[2/3] + Sqrt[a z] (3^(1/3) E^((2/3) (a z)^(3/2)) + (a^3 z^3 BesselI[-(4/3), (2/3) a^(3/2) z^(3/2)] Gamma[2/3])/ (a^(3/2) z^(3/2))^(2/3) - a z (a^(3/2) z^(3/2))^(2/3) BesselI[4/3, (2/3) a^(3/2) z^(3/2)] Gamma[2/3])))/ E^((2/3) (a z)^(3/2)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SqrtBox["z"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], " ", RowBox[List["AiryAi", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["15", " ", SuperscriptBox["a", "2"], " ", SqrtBox["z"], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]]]]], RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["AiryAi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["a", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["4", "3"]]], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["2", "/", "3"]]]], "-", RowBox[List["a", " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["4", "3"], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 z 1 3 ( - 2 ) ( a z ) 3 / 2 Ai ( a z ) z 1 15 a 2 z Γ ( 2 3 ) ( 2 1 3 ( - 2 ) ( a z ) 3 / 2 ( 3 a 2 Ai ( a z ) Γ ( 2 3 ) z 2 + a z ( - a z I 4 3 ( 2 3 a 3 / 2 z 3 / 2 ) Γ ( 2 3 ) ( a 3 / 2 z 3 / 2 ) 2 / 3 + 3 3 2 3 ( a z ) 3 / 2 + a 3 z 3 Γ ( 2 3 ) ( a 3 / 2 z 3 / 2 ) 2 / 3 I - 4 3 ( 2 3 a 3 / 2 z 3 / 2 ) ) ) ) z z 1 2 1 3 -2 a z 3 2 AiryAi a z 1 15 a 2 z 1 2 Gamma 2 3 -1 2 1 3 -2 a z 3 2 3 a 2 AiryAi a z Gamma 2 3 z 2 a z 1 2 -1 a z BesselI 4 3 2 3 a 3 2 z 3 2 Gamma 2 3 a 3 2 z 3 2 2 3 3 1 3 2 3 a z 3 2 a 3 z 3 Gamma 2 3 a 3 2 z 3 2 2 3 -1 BesselI -1 4 3 2 3 a 3 2 z 3 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SqrtBox["z_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a_", " ", "z_"]], ")"]], RowBox[List["3", "/", "2"]]]]]], " ", RowBox[List["AiryAi", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["AiryAi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["a", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["4", "3"]]], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["2", "/", "3"]]]], "-", RowBox[List["a", " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["4", "3"], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["15", " ", SuperscriptBox["a", "2"], " ", SqrtBox["z"], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]]]]]]]]]

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

 2001-10-29