Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Exceptional $ q$-Askey-Wilson polynomials and continued fractions

Authors: Dharma P. Gupta and David R. Masson
Journal: Proc. Amer. Math. Soc. 112 (1991), 717-727
MSC: Primary 33D45; Secondary 39A10, 40A15
MathSciNet review: 1059625
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Two linearly independent solutions of the three-term recurrence relation for the $ q$-Askey-Wilson polynomials are obtained for the special cases $ abcd = {q^m},m = 1,2, \ldots $.By obtaining the subdominant solution and employing Pincherle's theorem, the associated continued fractions and properties of the corresponding weight functions are derived. The cases $ abcd = q\;{\text{or}}\;{q^2}$ are exceptional. They differ from the cases considered by Askey and Wilson [1 ] and are limits of a family of associated cases considered by Ismail and Rahman [5].

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 33D45, 39A10, 40A15

Retrieve articles in all journals with MSC: 33D45, 39A10, 40A15

Additional Information

PII: S 0002-9939(1991)1059625-X
Keywords: Askey-Wilson polynomials, three-term recurrence, subdominant solution, Pincherle's theorem, continued fractions, weight functions, mass points
Article copyright: © Copyright 1991 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia