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Convergence of series, sequences and functions and different modes of convergence.
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Asymptotic behavior of the Hermite functions
I would like to understand the asymptotic behavior of the Hermite function :
$$\psi_k(x) = \frac{1}{\sqrt{2^k k!}}H_k(x) e^{-\frac{x^2}{2}},$$
where $H_k(x)$ is the $k-$th Hermite polynomial. For inst …