New bounds on the Hermite polynomials

Ilia Krasikov

New bounds on the Hermite polynomials

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arxiv math/0401310 v1 pith:M3EUHVOD submitted 2004-01-23 math.CA

Ilia Krasikov This is my paper · ORCID

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keywords hermitepolynomialsasymptoticallyaxisboundsconstantestablishexplicit

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abstract

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

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