Representing by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials

被引：0
作者：
Taekyun Kim
Dae San Kim
Lee-Chae Jang
D. V. Dolgy
机构：
[1] Kwangwoon University,Department of Mathematics
[2] Sogang University,Department of Mathematics
[3] Konkuk University,Graduate School of Education
[4] Kwangwoon University,Hanrimwon
来源：
Advances in Difference Equations | / 2019卷
关键词：
Lucas polynomials; Chebyshev polynomials of the first kind; Sums of finite products; Orthogonal polynomials;
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摘要：
In this paper, we investigate sums of finite products of Chebyshev polynomials of the first kind and those of Lucas polynomials. We express each of them as linear combinations of Hermite, extended Laguerre, Legendre, Gegenbauer, and Jacobi polynomials whose coefficients involve some terminating hypergeometric functions F11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${}_{1}F_{1}$\end{document} and F12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${}_{2}F_{1}$\end{document}. These are obtained by means of explicit computations.
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