Acta mathematica scientia, Series B >
A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS
Received date: 2006-08-14
Revised date: 1900-01-01
Online published: 2008-10-20
In this article, the author extends the validity of a uniform asymptotic expansion of the Hermite polynomials Hn(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
Shi Wei . A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS[J]. Acta mathematica scientia, Series B, 2008 , 28(4) : 834 -842 . DOI: 10.1016/S0252-9602(08)60084-3
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