Orthogonal polynomials

Discrete mathematics

Pure mathematics

Classical orthogonal polynomials

Mathematics

Gegenbauer polynomials

Fibonacci polynomials

Chebyshev polynomials

Algebra over a field

Mathematical analysis

Fibonacci number

Fourier series

Lucas number

Wilson polynomials

Discrete orthogonal polynomials

Jacobi polynomials

Hahn polynomials

Difference polynomials

Journal of Inequalities and Applications

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.

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