Table of Contents
ISRN Algebra
Volume 2011, Article ID 268096, 18 pages
http://dx.doi.org/10.5402/2011/268096
Research Article

Sequences of Non-Gegenbauer-Humbert Polynomials Meet the Generalized Gegenbauer-Humbert Polynomials

1Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL 61702, USA
2Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020, USA

Received 19 April 2011; Accepted 12 May 2011

Academic Editors: F. Kittaneh, L. Vinet, and A. Vourdas

Copyright © 2011 Tian-Xiao He and Peter J.-S. Shiue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Here, we present a connection between a sequence of polynomials generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known transfer formulas between non-Gegenbauer-Humbert polynomials and generalized Gegenbauer-Humbert polynomials are given. The applications of the relationship to the construction of identities of polynomial sequences defined by linear recurrence relations are also discussed.