Abstract
In this article, the author extends the validity of a uniform asymptotic expansion of the Hermite polynomials H n ( 2 n + 1 α ) 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.
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