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AiryBiPrime






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.08.21.0032.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Cosh[b + (2/3) (a z)^(3/2)] AiryBiPrime[a z], z] == (z^\[Alpha] (9 (2 + \[Alpha]) Gamma[5/3] HypergeometricPFQ[ {-(1/6), (2 \[Alpha])/3}, {-(1/3), 1 + (2 \[Alpha])/3}, (-(4/3)) (a z)^(3/2)] + 9 E^(2 b) (2 + \[Alpha]) Gamma[5/3] HypergeometricPFQ[{-(1/6), (2 \[Alpha])/3}, {-(1/3), 1 + (2 \[Alpha])/3}, (4/3) (a z)^(3/2)] + 3^(2/3) a^2 z^2 \[Alpha] Gamma[1/3] (HypergeometricPFQ[{7/6, 4/3 + (2 \[Alpha])/3}, {7/3, 7/3 + (2 \[Alpha])/3}, (-(4/3)) (a z)^(3/2)] + E^(2 b) HypergeometricPFQ[{7/6, 4/3 + (2 \[Alpha])/3}, {7/3, 7/3 + (2 \[Alpha])/3}, (4/3) (a z)^(3/2)])))/E^b/ (6 3^(5/6) \[Alpha] (2 + \[Alpha]) Gamma[1/3] Gamma[5/3])










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