Asymptotics of Racah polynomials with fixed parameters

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

1 Scopus Citations
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Author(s)

  • X.-S. WANG
  • R. WONG

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)1083-1096
Journal / PublicationProceedings of the American Mathematical Society
Volume146
Issue number3
Online published28 Sept 2017
Publication statusPublished - Mar 2018

Abstract

In this paper, we investigate asymptotic behaviors of Racah polynomials with fixed parameters and scaled variable as the polynomial degree tends to infinity. We start from the difference equation satisfied by the polynomials
and derive an asymptotic formula in the outer region via ratio asymptotics.
Next, we find the asymptotic formulas in the oscillatory region via a simple matching principle. Unlike the varying parameter case considered in a previous paper, the zeros of Racah polynomials with fixed parameters may not
always be real. For this unusual case, we also provide a standard method to determine the oscillatory curve which attracts the zeros of Racah polynomials
when the degree becomes large.

Research Area(s)

  • Asymptotics, Racah polynomials, difference equations, matching principle

Citation Format(s)

Asymptotics of Racah polynomials with fixed parameters. / WANG, X.-S. ; WONG, R.
In: Proceedings of the American Mathematical Society, Vol. 146, No. 3, 03.2018, p. 1083-1096.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review