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AiryAiPrime






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryAiPrime[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/03.07.06.0043.01









  


  










Input Form





AiryAiPrime[z] \[Proportional] (-(1/(4 Sqrt[6 Pi] (-z^3)^(7/12)))) ((((-1 + Sqrt[3]) z^2 - (-1 + Sqrt[3]) z^(3/2) (-z^3)^(1/6) + (1 + Sqrt[3]) Sqrt[z] Sqrt[-z^3] + (1 + Sqrt[3]) (-z^3)^(2/3))/ E^((2 z^(3/2))/3) + E^((2 z^(3/2))/3) ((-1 + Sqrt[3]) z^2 + (-1 + Sqrt[3]) z^(3/2) (-z^3)^(1/6) - (1 + Sqrt[3]) Sqrt[z] Sqrt[-z^3] + (1 + Sqrt[3]) (-z^3)^(2/3))) HypergeometricPFQ[{-(1/12), 5/12, 7/12, 13/12}, {1/2}, 9/(4 z^3)] - (7/(48 (-z^3)^(1/2))) (((1 + Sqrt[3]) z^2 + (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/6) + (1 - Sqrt[3]) Sqrt[z] Sqrt[-z^3] - (1 - Sqrt[3]) (-z^3)^(2/3))/E^((2 z^(3/2))/3) + E^((2 z^(3/2))/3) ((1 + Sqrt[3]) z^2 - (1 + Sqrt[3]) z^(3/2) (-z^3)^(1/6) - (1 - Sqrt[3]) Sqrt[z] Sqrt[-z^3] - (1 - Sqrt[3]) (-z^3)^(2/3))) HypergeometricPFQ[ {5/12, 11/12, 13/12, 19/12}, {3/2}, 9/(4 z^3)]) /; (Abs[z] -> Infinity)










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02





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