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

Advances in Difference Equations

卷:2019

Taekyun Kim¹  Dae San Kim²  Lee-Chae Jang³  D. V. Dolgy⁴ 

[1] Department of Mathematics, Kwangwoon University;

[2] Department of Mathematics, Sogang University;

[3] Graduate School of Education, Konkuk University;

[4] Hanrimwon, Kwangwoon University;

关键词: Lucas polynomials;    Chebyshev polynomials of the first kind;    Sums of finite products;    Orthogonal polynomials;   

DOI  :  10.1186/s13662-019-2092-6

来源: DOAJ

【 摘 要 】

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 F11 ${}_{1}F_{1}$ and F12 ${}_{2}F_{1}$. These are obtained by means of explicit computations.

【 授权许可】

Unknown