Abstract:

In this article, the author extends the validity of a uniform asymptotic expansion of the Hermite polynomials H_n(2n+1α) to include all positive values of α. His method makes use of the rational functions introduced by Olde Daalhuis and Temme (SIAM J. Math. Anal., (1994), 25: 304-321). A new estimate for the remainder is given.

Key words: Hermite polynomials, uniform asymptotic expansion, Airy function