Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials

Abstract

Abstract In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we can express those sums of finite products in terms of Bernoulli polynomials and obtain some identities by using those expressions.

Keywords

• Fourier series
• Chebyshev polynomials of the second kind
• Fibonacci polynomials