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New bounds on the Hermite polynomials

经典分析与常微分方程 2007-05-23 v1

摘要

We shall establish two-side explicit inequalities, which are asymptotically sharp up to a constant factor, on the maximum value of Hk(x)ex2/2,|H_k(x)| e^{-x^2/2}, on the real axis, where HkH_k are the Hermite polynomials.

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引用

@article{arxiv.math/0401310,
  title  = {New bounds on the Hermite polynomials},
  author = {Ilia Krasikov},
  journal= {arXiv preprint arXiv:math/0401310},
  year   = {2007}
}