Abstract
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 {}_{1}F_{1} and {}_{2}F_{1}. These are obtained by means of explicit computations.
Highlights
1 Introduction and preliminaries we will first fix some notations that will be used throughout this paper and recall the necessary basic facts about orthogonal polynomials
As we will limit the facts to the minimum, the interested reader is advised to refer to general books on orthogonal polynomials, for example [2, 4]
The purpose of this paper is to study the sums of finite products of Chebyshev polynomials of the first kind in (1.33) and those of Lucas polynomials in (1.34), and to express each of them as linear combinations of Hermite, extended Laguerre, Legendre, Gegenbauer, and Jacobi polynomials
Summary
We will first fix some notations that will be used throughout this paper and recall the necessary basic facts about orthogonal polynomials. As we will limit the facts to the minimum, the interested reader is advised to refer to general books on orthogonal polynomials, for example [2, 4]. For any nonnegative integer n, the falling factorial polynomials (x)n and the rising factorial polynomials x n are respectively given by (x)n = x(x – 1) · · · (x – n + 1) (n ≥ 1), (x)0 = 1, (1.1). The two factorial polynomials are related by (–1)n(x)n = –x n, (–1)n x n = (–x)n,. =. 22n–2j(–1)j n j n (n ≥ j ≥ 0),.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
