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

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SUMMARY

The discussion focuses on solving the limits of the Airy functions AiryAi and AiryBi as y approaches infinity. Specifically, the limit for AiryAi converges to 0, while AiryBi diverges to infinity when evaluated at the expression AiryAi(k² + s + γ(y - b)k / (-k²/3γ²/3)). The user utilized Maple and Mathematica to derive these results from differential equations. Additionally, the user inquires about the feasibility of performing Fourier transformations on Airy functions.

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germana2006
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I have to solve the limit for the following Airy function in the case when [tex]y\rightarrow{}\infty[/tex]:
[tex]AiryAi(\frac{k^2+s+\gamma(y-b)k}{(-k^{2/3}\gamma^{2/3})})[/tex]

and also for the following function

[tex]AiryBi(\frac{k^2+s+\gamma(y-b)k}{(-k^{2/3}\gamma^{2/3})})[/tex]
 
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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.
 
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?
 

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