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AiryAi






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.05.06.0019.01









  


  










Input Form





AiryAi[-z] \[Proportional] (1/(Sqrt[Pi] z^(1/4))) (Sin[(2 z^(3/2))/3 + Pi/4] Sum[((Pochhammer[1/12, k] Pochhammer[5/12, k] Pochhammer[7/12, k] Pochhammer[11/12, k])/(Pochhammer[1/2, k] k!)) (-(9/(4 z^3)))^k, {k, 0, Infinity}] - (5/(48 z^(3/2))) Cos[(2 z^(3/2))/3 + Pi/4] Sum[((Pochhammer[7/12, k] Pochhammer[11/12, k] Pochhammer[13/12, k] Pochhammer[17/12, k])/(Pochhammer[3/2, k] k!)) (-(9/(4 z^3)))^k, {k, 0, Infinity}]) /; Abs[Arg[z]] < (2 Pi)/3 && (Abs[z] -> Infinity)










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)





2003-08-21





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