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http://functions.wolfram.com/03.06.21.0026.01
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Integrate[Cosh[(2/3) (a z^r)^(3/2)] AiryBi[a z^r], 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)] +
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)] +
HypergeometricPFQ[{5/6, 2/3 + 2/(3 r)}, {5/3, 5/3 + 2/(3 r)},
(4/3) (a z^r)^(3/2)])))/(2 3^(5/6) (1 + r) Gamma[2/3] Gamma[4/3])
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/> <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> <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'> 4 <sep /> 3 </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> <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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