Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Connection Problem for Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds

Version 1 : Received: 8 October 2018 / Approved: 8 October 2018 / Online: 8 October 2018 (11:20:20 CEST)

A peer-reviewed article of this Preprint also exists.

Dolgy, D.V.; Kim, D.S.; Kim, T.; Kwon, J. Connection Problem for Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds. Symmetry 2018, 10, 617. Dolgy, D.V.; Kim, D.S.; Kim, T.; Kwon, J. Connection Problem for Sums of Finite Products of Chebyshev Polynomials of the Third and Fourth Kinds. Symmetry 2018, 10, 617.

Journal reference: Symmetry 2018, 10, 617
DOI: 10.3390/sym10110617

## Abstract

This paper treats the connection problem of expressing sums of finite products of Chebyshev polynomials of the third and fourth kinds in terms of five classical orthogonal polynomials. In fact, by carrying out explicit computations each of them are expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer, and Jacobi polynomials which involve some terminating hypergeometric functions ${}_2 F_0, {}_2 F_1$, and ${}_3 F_2$.

## Keywords

sums of finite products of chebyshev polynomials of the third and fourth kinds; Hermite; generalized Laguerre; Legendre; Gegenbauer; Jacobi

## Subject

MATHEMATICS & COMPUTER SCIENCE, Analysis

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