A globally uniform asymptotic expansion of the hermite polynomials

In this article, the author extends the validity of a uniform asymptotic expansion of the Hermite polynomials 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.