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AiryBiPrime






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryBiPrime[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/03.08.21.0067.01









  


  










Input Form





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










Standard Form





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MathML Form







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</ci> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </list> <list> <cn type='rational'> 1 <sep /> 3 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='rational'> 2 <sep /> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <pi /> <apply> <ci> MeijerG </ci> <list> <list> <cn type='rational'> 1 <sep /> 3 </cn> <cn type='rational'> 5 <sep /> 6 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; 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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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