Asymptotic analysis of a family of polynomials associated with the inverse error function

2008/11/13 by Diego Dominici, Dominici, Diego, Charles Knessl +1
Mathematics · #33B20 (primary) 34E20 #33E30 (secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33B20 #msc:33E30 #msc:34E20

paper · pdf · doi:10.48550/arxiv.0811.2243

26 pages, 7 figures

arxiv created 2008/11/13 · arxiv updated 2009/12/01

Abstract

We analyze the sequence of polynomials defined by the differential-difference equation P_n+1(x)=P_n^′(x)+x(n+1)P_n(x) asymptotically as n→∞. The polynomials P_n(x) arise in the computation of higher derivatives of the inverse error function inverf(x). We use singularity analysis and discrete versions of the WKB and ray methods and give numerical results showing the accuracy of our formulas.

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• Asymptotic distribution of zeros of polynomials satisfying difference equations
• Hyperasymptotics for linear difference equations with an irregular singularity of rank one: Polynomial coefficients