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AiryAi






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryAi[z] > Series representations > Asymptotic series expansions > Expansions inside Stokes sectors > In exponential form





http://functions.wolfram.com/03.05.06.0036.01









  


  










Input Form





AiryAi[z] \[Proportional] (1/(E^((2 z^(3/2))/3) (2 Sqrt[Pi] z^(1/4)))) (Sum[((Pochhammer[1/12, k] Pochhammer[7/12, k] Pochhammer[5/12, k] Pochhammer[11/12, k])/(Pochhammer[1/2, k] k!)) (9/(4 z^3))^k, {k, 0, n}] + O[1/z^(3 (n + 1))]) - (5/(E^((2 z^(3/2))/3) (96 Sqrt[Pi] z^(7/4)))) (Sum[((Pochhammer[7/12, k] Pochhammer[13/12, k] Pochhammer[11/12, k] Pochhammer[17/12, k])/(k! Pochhammer[3/2, k])) (9/(4 z^3))^k, {k, 0, n}] + O[1/z^(3 (n + 1))]) /; Abs[Arg[z]] < Pi && (Abs[z] -> Infinity) && Element[n, Integers] && n >= 0










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)





2007-05-02