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AiryAi






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryAi[z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/03.05.21.0077.01









  


  










Input Form





Integrate[t^(\[Alpha] - 1) AiryAi[t]^2, {t, 0, Infinity}] == (2^((1/3) (-5 - 2 \[Alpha])) 3^((1/6) (-11 - 2 \[Alpha])) Gamma[1/6 - \[Alpha]/3] (3^\[Alpha] Gamma[\[Alpha]/3] Gamma[(1 + \[Alpha])/3] - 2 Sqrt[3] Gamma[1/3 - \[Alpha]/3] Gamma[\[Alpha]] Sin[(Pi \[Alpha])/3]))/ (Pi^(3/2) Gamma[1/3 - \[Alpha]/3]) /; Re[\[Alpha]] > 0










Standard Form





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MathML Form







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</ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> AiryAi </ci> <ci> t </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#945; </ci> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <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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