Title

Plancherel-Rotach Asymptotics For Q-Orthogonal Polynomials

Keywords

Asymptotics; Error terms; q-Orthogonal polynomials; Ramanujan function; Recurrence relations

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. © 2013 Springer Science+Business Media New York.

Publication Date

6-1-2013

Publication Title

Constructive Approximation

Volume

37

Issue

3

Number of Pages

341-356

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00365-013-9182-6

Socpus ID

84877799329 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84877799329

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