Solving Airy Functions for Limit as y $\rightarrow$ $\infty$

[germana2006]

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})})

 

[HallsofIvy]

Yes, and I don't! I will, however, be happy to help you as soon as you show exactly where you need help. What is the definition of the Airy functions? That's always a good place to start.

 

[germana2006]

I am not experte in Airy function. I become this solution in Maple and Mathematica from a differential equation.
I have look in some books the definition and now I have the solution for this limits. They go to 0 for AiryAi and to infinity for AiryBi.
My question now, is it possible to do the Fourier transformation and the inverse Fourier transformation of the Airy functions?