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AiryBi






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryBi[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions and a power function > Involving sinh and power > Linear argument





http://functions.wolfram.com/03.06.21.0028.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Sinh[(2/3) (a z)^(3/2)] AiryBi[a z], z] == -(z^\[Alpha] (3^(2/3) (1 + \[Alpha]) Gamma[4/3] HypergeometricPFQ[ {1/6, (2 \[Alpha])/3}, {1/3, 1 + (2 \[Alpha])/3}, (-(4/3)) (a z)^(3/2)] - 3^(2/3) (1 + \[Alpha]) Gamma[4/3] HypergeometricPFQ[{1/6, (2 \[Alpha])/3}, {1/3, 1 + (2 \[Alpha])/3}, (4/3) (a z)^(3/2)] + a z \[Alpha] Gamma[2/3] (HypergeometricPFQ[{5/6, 2/3 + (2 \[Alpha])/3}, {5/3, 5/3 + (2 \[Alpha])/3}, (-(4/3)) (a z)^(3/2)] - HypergeometricPFQ[{5/6, 2/3 + (2 \[Alpha])/3}, {5/3, 5/3 + (2 \[Alpha])/3}, (4/3) (a z)^(3/2)])))/ (2 3^(5/6) \[Alpha] (1 + \[Alpha]) Gamma[2/3] Gamma[4/3])










Standard Form





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MathML Form







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Rule Form





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





2001-10-29





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