Title

Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials

Authors

Authors

M. E. H. Ismail;X. Li

Comments

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Abbreviated Journal Title

Constr. Approx.

Keywords

q-Orthogonal polynomials; Asymptotics; Recurrence relations; Ramanujan; function; Error terms; VARYING RECURRENCE COEFFICIENTS; Mathematics

Abstract

We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q (-1)-Hermite polynomials of Askey, Ismail, and Masson; q-Laguerre polynomials; and the Stieltjes-Wigert polynomials. We also introduce a one-parameter family of solutions to the q-difference equation of the Ramanujan function.

Journal Title

Constructive Approximation

Volume

37

Issue/Number

3

Publication Date

1-1-2013

Document Type

Article

DOI Link

http://dx.doi.org/10.1007/s00365-013-9182-6

Language

English

First Page

341

Last Page

356

WOS Identifier

WOS:000319021000002

ISSN

0176-4276

Recommended Citation

"Plancherel-Rotach Asymptotics for q-Orthogonal Polynomials" (2013). Faculty Bibliography 2010s. 4142.
https://stars.library.ucf.edu/facultybib2010/4142