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AiryAi




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.05.06.0009.01









  


  








Input Form





AiryAi[z] \[Proportional] (1/((-z^3)^(5/12) (2 Sqrt[3 Pi]))) (((-1)^(1/12) ((-z^3)^(1/3) - (-1)^(1/3) z) HypergeometricPFQ[{1/6, 5/6}, {}, (3 I)/(4 Sqrt[-z^3])])/E^((2/3) I Sqrt[-z^3]) + (E^((2/3) I Sqrt[-z^3]) ((-z^3)^(1/3) + (-1)^(2/3) z) HypergeometricPFQ[{1/6, 5/6}, {}, -((3 I)/(4 Sqrt[-z^3]))])/ (-1)^12^(-1)) /; (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)





2001-10-29