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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 > Involving cosh > Linear argument





http://functions.wolfram.com/03.08.21.0024.01









  


  










Input Form





Integrate[Cosh[b + (2/3) (a z)^(3/2)] AiryBiPrime[a z], z] == (E^(-b - (2/3) (a z)^(3/2)) (-6 (-1 + E^(2 b + (4/3) (a z)^(3/2))) (a z)^(3/2) (a^(3/2) z^(3/2))^(2/3) AiryBi[a z] Gamma[5/3] + 15 a (1 + E^(2 b + (4/3) (a z)^(3/2))) z (a^(3/2) z^(3/2))^(2/3) AiryBiPrime[a z] Gamma[5/3] - Sqrt[3] (3 a^3 (1 + E^(2 b + (4/3) (a z)^(3/2))) z^3 BesselI[-(4/3), (2/3) a^(3/2) z^(3/2)] Gamma[5/3] + (a^(3/2) z^(3/2))^(1/3) (2 3^(1/3) E^((2/3) (a z)^(3/2)) (1 + E^(2 b)) (a^(3/2) z^(3/2))^(1/3) + 3 a^(5/2) (1 + E^(2 b + (4/3) (a z)^(3/2))) z^(5/2) BesselI[4/3, (2/3) a^(3/2) z^(3/2)] Gamma[5/3]))))/ (30 a (a^(3/2) z^(3/2))^(2/3) Gamma[5/3])










Standard Form





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MathML Form







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<power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -6 </cn> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='rational'> 4 <sep /> 3 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <cn type='rational'> 3 <sep 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</apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <ci> z </ci> <apply> <power /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <ci> AiryBiPrime </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='rational'> 4 <sep /> 3 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <ci> BesselI </ci> <cn type='rational'> 4 <sep /> 3 </cn> <apply> <times /> <cn type='rational'> 2 <sep /> 3 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='rational'> 2 <sep /> 3 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='rational'> 4 <sep /> 3 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> BesselI </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 3 </cn> </apply> <apply> <times /> <cn type='rational'> 2 <sep /> 3 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 3 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.