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

2006/01/04 by Diego Dominici, Dominici, Diego · 1 citation
Mathematics · #Differential Equations and Numerical Methods #Mathematical functions and polynomials #Numerical methods for differential equations #math.CA #msc:33C45 #msc:34E05 #msc:34E20

paper · pdf · doi:10.48550/arxiv.math/0601078

21 pages, 2 figures

arxiv created 2006/01/04 · arxiv updated 2009/12/01

Abstract

We analyze the Hermite polynomials H_n(x) and their zeros asymptotically, as n→∞. 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.

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