A simple approach to q-Chebyshev polynomials

Abstract

It is shown that some q-analogues of the Fibonacci and Lucas polynomials lead to q-analogues of the Chebyshev polynomials which retain most of their elementary properties.

29 pages, Rodrigues-type formulae have been added

References in corpus (2)

• A noncommutative weight-dependent generalization of the binomial theorem
• Some beautiful q-analogues of Fibonacci and Lucas polynomials

Cited by in corpus (6)

• Additions to the formula lists in "Hypergeometric orthogonal polynomials and their $q$-analogues" by Koekoek, Lesky and Swarttouw
• q-Chebyshev polynomials
• Hankel determinants of some polynomial sequences
• Some remarks about q-Chebyshev polynomials and q-Catalan numbers and related results
• A graphical categorification of the two-variable Chebyshev polynomials of the second kind
• Elementary observations on Rogers-Szegö polynomials