Preprint Article Version 1 This version is not peer-reviewed

# Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials

Version 1 : Received: 7 September 2018 / Approved: 14 September 2018 / Online: 14 September 2018 (10:17:50 CEST)

A peer-reviewed article of this Preprint also exists.

Kim, T.; Kim, D.S.; Kwon, J.; Dolgy, D.V. Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials. Mathematics 2018, 6, 210. Kim, T.; Kim, D.S.; Kwon, J.; Dolgy, D.V. Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials. Mathematics 2018, 6, 210.

Journal reference: Mathematics 2018, 6, 210
DOI: 10.3390/math6100210

## Abstract

This paper is concerned with representing sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials. Indeed, by explicit computations each of them is expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials which involve the hypergeometric functions ${}_1 F_1$ and ${}_2 F_1$.

## Subject Areas

Chebyshev polynomials of second kind; Fibonacci polynomials; sums of finite products; orthogonal polynomials