SCHWEITZER 1953 Problem 6

Let $H_{n}(x)$ be the nth Hermite polynomial. Find $\lim_{n \to \infty } (\frac{y}{2n})^{n} H_{n}(\frac{n}{y})$ For an arbitrary real y. (S.5) $H_n(x)=(-1)^n e^{x^2}\frac{d^n}{dx^n}\left(e^{{-x^2}}\right)$