English

Asymptotic analysis of the Hermite polynomials from their differential-difference equation

Classical Analysis and ODEs 2007-05-23 v1

Abstract

We analyze the Hermite polynomials Hn(x)H_{n}(x) and their zeros asymptotically, as n.n\to\infty. We obtain asymptotic approximations from the differential-difference equation which they satisfy, using the ray method. We give numerical examples showing the accuracy of our formulas.

Keywords

Cite

@article{arxiv.math/0601078,
  title  = {Asymptotic analysis of the Hermite polynomials from their differential-difference equation},
  author = {Diego Dominici},
  journal= {arXiv preprint arXiv:math/0601078},
  year   = {2007}
}

Comments

21 pages, 2 figures

R2 v1 2026-07-22T17:29:29.781Z