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http://functions.wolfram.com/03.08.21.0015.01
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Integrate[z^(\[Alpha] - 1) E^((2/3) (a z)^(3/2)) AiryBiPrime[a z], z] ==
(1/(\[Alpha] Gamma[1/3])) (3^(1/6) z^\[Alpha] HypergeometricPFQ[
{-(1/6), (2 \[Alpha])/3}, {-(1/3), 1 + (2 \[Alpha])/3},
(4/3) (a z)^(3/2)]) + (a^2 z^(2 + \[Alpha])
HypergeometricPFQ[{7/6, 4/3 + (2 \[Alpha])/3},
{7/3, 7/3 + (2 \[Alpha])/3}, (4/3) (a z)^(3/2)])/
(3 3^(1/6) (2 + \[Alpha]) Gamma[5/3])
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mrow> <msup> <mi> z </mi> <mrow> <mi> α </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> Bi </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mfrac> <mrow> <mroot> <mn> 3 </mn> <mn> 6 </mn> </mroot> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> α </mi> </msup> </mrow> <mrow> <mi> α </mi> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> 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<mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mn> 3 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 4 </mn> <mn> 3 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 3 </mn> </mfrac> <mo> , </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> α </mi> </mrow> <mn> 3 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 7 </mn> <mn> 3 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 4 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "6"], 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</mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> α </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='rational'> 2 <sep /> 3 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> AiryBiPrime </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <apply> <power /> <ci> z </ci> <ci> α </ci> </apply> <apply> <power /> <apply> <times /> <ci> α </ci> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <apply> <times /> <cn type='rational'> 4 <sep /> 3 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> α </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <apply> <plus /> <ci> α </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 7 <sep /> 6 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 4 <sep /> 3 </cn> </apply> </list> <list> <cn type='rational'> 7 <sep /> 3 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> α </ci> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 7 <sep /> 3 </cn> </apply> </list> <apply> <times /> <cn type='rational'> 4 <sep /> 3 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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