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
Copyright Status
Unknown
Socpus ID
84877799329 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84877799329
STARS Citation
Ismail, Mourad E.H. and Li, Xin, "Plancherel-Rotach Asymptotics For Q-Orthogonal Polynomials" (2013). Scopus Export 2010-2014. 7048.
https://stars.library.ucf.edu/scopus2010/7048