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Math Help - Airy function

  1. #1
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    Airy function

    I have to solve the limit for the following Airy function in the case when y\rightarrow{}\infty:
    AiryAi(\frac{k^2+s+\gamma(y-b)k}{(-k^{2/3}\gamma^{2/3})})

    and also for the following function

    AiryBi(\frac{k^2+s+\gamma(y-b)k}{(-k^{2/3}\gamma^{2/3})})
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Airyai(x) do you mean \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{xy+\frac{y^3}{3}}dy?
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  3. #3
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    I have not idea about the Airy function. I become the Airy function as a result of a differential equation with Maple and then I have to do this limit for this solution to be able to continue with my calculations.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by germana2006 View Post
    I have to solve the limit for the following Airy function in the case when y\rightarrow{}\infty:
    AiryAi(\frac{k^2+s+\gamma(y-b)k}{(-k^{2/3}\gamma^{2/3})})

    and also for the following function

    AiryBi(\frac{k^2+s+\gamma(y-b)k}{(-k^{2/3}\gamma^{2/3})})
    Assuming \gamma k >0 you want the \lim_{x \to -\infty} {\rm{Ai}}(x), and \lim_{x \to -\infty} {\rm{Bi}}(x) which are respectivly 0 and 0.

    RonL
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  5. #5
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    Thank you very much.

    If I try to do in Mathematica the inverse fourier transformation for the Airy function respect to k or k^2, it is possible. But for more complicated arguments in the Airy function like I have writen in my first post, it is not possible with Mathematica or Maple. Is it possible to do the inverse Fourier Transform for this type of Airy functions or other more complicated?.
    If yes, how?
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