Preprint Article Version 1 This version is not peer-reviewed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)

How to cite: 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. Preprints 2018, 2018090258 (doi: 10.20944/preprints201809.0258.v1). 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. Preprints 2018, 2018090258 (doi: 10.20944/preprints201809.0258.v1).

## 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 1F1 and 2F1.

## Subject Areas

Chebyshev polynomials of second kind, Fibonacci polynomials, sums of finite products, orthogonal polynomials.