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http://functions.wolfram.com/03.06.21.0012.01
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Integrate[AiryBi[a z^r]/E^((2/3) (a z^r)^(3/2)), z] ==
(z (3^(2/3) (1 + r) Gamma[4/3] HypergeometricPFQ[{1/6, 2/(3 r)},
{1/3, 1 + 2/(3 r)}, (-(4/3)) (a z^r)^(3/2)] +
a z^r Gamma[2/3] HypergeometricPFQ[{5/6, 2/3 + 2/(3 r)},
{5/3, 5/3 + 2/(3 r)}, (-(4/3)) (a z^r)^(3/2)]))/
(3^(5/6) (1 + r) Gamma[2/3] Gamma[4/3])
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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> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> Bi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msup> <mn> 3 </mn> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 6 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> 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</mfrac> <mo> + </mo> <mfrac> <mn> 2 </mn> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </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["5", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["2", "3"], "+", FractionBox["2", RowBox[List["3", " ", "r"]]]]], 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<mn> 3 </mn> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 4 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 2 </mn> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 2 </mn> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </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["1", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["2", RowBox[List["3", " ", "r"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "+", FractionBox["2", RowBox[List["3", " ", "r"]]]]], 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</ci> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> AiryBi </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 5 <sep /> 6 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 4 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <ci> Gamma </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 5 <sep /> 6 </cn> <apply> <plus /> <cn type='rational'> 2 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> <list> <cn type='rational'> 5 <sep /> 3 </cn> <apply> <plus /> <cn type='rational'> 5 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <cn type='integer'> -4 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 4 <sep /> 3 </cn> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </list> <list> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <cn type='integer'> -4 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </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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