Does anybody know how to proof the first asymptotic expansion of this page:
http://en.wikipedia.org/wiki/Hermite_polynomials#Asymptotic_expansion ? (and how the physicist use this asymptotic expansion ?)
I try to use the expression of $H_n$, the Hermite polynomial:
$ H_n(x)= \frac{i^n e^{x^2}}{2 \sqrt{\pi}} \int_{R}t^n e^{-t^2/4}e^{-ixt}dt$ with the Laplace's method like for the asymptotic expansion of $H_n(\frac{x}{\sqrt{2n}}) $ but I failed.
Thanks in advance.