Chebyshev-Fibonacci polynomial relations using generating functions

Abstract

The main object of the paper is to reveal connections between Chebyshev polynomials of the fi rst and second kinds and Fibonacci polynomials introduced by Catalan. This is achieved by relating the respective (ordinary and exponential) generating functions to each other. As a consequence, we also establish new combinatorial identities for balancing polynomials and Fibonacci (Lucas) numbers.