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AiryAi




Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryAi[z] > Series representations > Asymptotic series expansions > Expansions for any z in trigonometric form > Using trigonometric functions with branch cut-containing arguments





http://functions.wolfram.com/03.05.06.0023.01









  


  








Input Form





AiryAi[z] \[Proportional] (1/(2 Sqrt[3 Pi] (-z^3)^(5/12))) ((Sqrt[3] (-z + (-z^3)^(1/3)) Cos[Pi/4 - (2 Sqrt[-z^3])/3] + (z + (-z^3)^(1/3)) Cos[Pi/4 + (2 Sqrt[-z^3])/3]) (1 + 385/(4608 z^3) + 37182145/(127401984 z^6) + O[1/z^9]) + (5/(48 Sqrt[-z^3])) ((z + (-z^3)^(1/3)) Cos[Pi/4 - (2 Sqrt[-z^3])/3] + Sqrt[3] (z - (-z^3)^(1/3)) Cos[Pi/4 + (2 Sqrt[-z^3])/3]) (1 + 17017/(13824 z^3) + 1078282205/(127401984 z^6) + O[1/z^9])) /; (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