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AiryAiPrime






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryAiPrime[z] > Integration > Indefinite integration > Involving direct function and Bessel-type functions > Involving Bessel functions > Involving Bessel K and power > Power arguments





http://functions.wolfram.com/03.07.21.0066.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) BesselK[\[Nu], (2/3) (a z^r)^(3/2)] AiryAiPrime[a z^r], z] == (1/2) Pi Csc[Pi \[Nu]] ((1/(Pi^(3/2) r)) (2^(-(5/3) + \[Nu]) 3^(-(5/6) - \[Nu]) z^\[Alpha] ((a z^r)^(3/2))^\[Nu] MeijerG[{{(1/6) (2 - 3 \[Nu]), (1/6) (5 - 3 \[Nu]), 1 - \[Alpha]/(3 r) - \[Nu]/2}, {}}, {{0, 2/3}, {2/3 - \[Nu], -\[Nu], -((2 \[Alpha] + 3 r \[Nu])/(6 r))}}, (2/3)^(2/3) a z^r, 1/3]) - (1/(Pi^(3/2) r)) ((2^(-(5/3) - \[Nu]) 3^(-(5/6) + \[Nu]) z^\[Alpha] MeijerG[{{1 - \[Alpha]/(3 r) + \[Nu]/2, (1/6) (2 + 3 \[Nu]), (1/6) (5 + 3 \[Nu])}, {}}, {{0, 2/3}, {-(\[Alpha]/(3 r)) + \[Nu]/2, \[Nu], 2/3 + \[Nu]}}, (2/3)^(2/3) a z^r, 1/3])/ ((a z^r)^(3/2))^\[Nu]))










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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