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arXiv · 1302.6196

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

Dan Dai·Mourad E. H. Ismail·Xiang-Sheng Wang
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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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Dan Dai, Mourad E. H. Ismail, Xiang-Sheng Wang. 2013-02-25. Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems. https://arxiv.org/abs/1302.6196

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