New bounds on the Hermite polynomials

We shall establish two-side explicit inequalities, which are asymptotically sharp up to a constant factor, on the maximum value of $\mathrm{\mid }{H}_k(x)\mathrm{\mid }{e}^{-x^2\mathrm{/}2},$ on the real axis, where $H_k$ are the Hermite polynomials.