Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems

2013/02/25 by Dai, Dan, Ismail, Mourad E. H., Wang, Xiang-Sheng · 1 citation
#33C47 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 41A60 #Secondary 30E05

paper · doi:10.48550/arxiv.1302.6196

Abstract

We study the Plancherel--Rotach asymptotics of four families of orthogonal polynomials, the Chen--Ismail polynomials, the Berg-Letessier-Valent polynomials, the Conrad--Flajolet polynomials I and II. All these polynomials arise in indeterminate moment problems and three of them are birth and death process polynomials with cubic or quartic rates. We employ a difference equation asymptotic technique due to Z. Wang and R. Wong. Our analysis leads to a conjecture about large degree behavior of polynomials orthogonal with respect to solutions of indeterminate moment problems.

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