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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-free arguments





http://functions.wolfram.com/03.05.06.0043.01









  


  










Input Form





AiryAi[z] \[Proportional] (1/(4 Sqrt[3 Pi])) ((1/((-z^3)^(5/12) (Sqrt[2] z^(3/2)))) (((-(-1 + Sqrt[3])) z^(5/2) + (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) + (1 + Sqrt[3]) z Sqrt[-z^3] - (-1 + Sqrt[3]) (-z^3)^(5/6))/ E^((2 z^(3/2))/3) - E^((2 z^(3/2))/3) ((-1 + Sqrt[3]) z^(5/2) - (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) + (1 + Sqrt[3]) z Sqrt[-z^3] - (-1 + Sqrt[3]) (-z^3)^(5/6))) HypergeometricPFQ[ {1/12, 5/12, 7/12, 11/12}, {1/2}, 9/(4 z^3)] + (5/(48 Sqrt[2] (-z^3)^(17/12))) (E^((2 z^(3/2))/3) ((-1 + Sqrt[3]) z^(5/2) - (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) + (1 + Sqrt[3]) z Sqrt[-z^3] - (-1 + Sqrt[3]) (-z^3)^(5/6)) - ((-1 + Sqrt[3]) z^(5/2) - (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/3) - (1 + Sqrt[3]) z Sqrt[-z^3] + (-1 + Sqrt[3]) (-z^3)^(5/6))/E^((2 z^(3/2))/3)) HypergeometricPFQ[ {7/12, 11/12, 13/12, 17/12}, {3/2}, 9/(4 z^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)





2007-05-02





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