I'm studying the Airy functions but i have some problem with the solutions.
Looking a "Asymptotic Expansions of Integrals by Bleistein and Handelsman" pag. 52
How i get the (2.5.9) is clear. I don't understand:
- Why we have to take $f_2(z) = e^{-2i\pi/3} Ai(ze^{-2i\pi/3}) $. The exponential outside is clear, but why i have $e^{-2i\pi/3}$ inside Ai? (same for $f_3(z)$)
- The (2.5.12). Why is $Bi = i[f_2(z) - f_3(z)]$?