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 1F1 and 2F1. These are obtained by means of explicit computations.
关键词：Lucas polynomials ; Chebyshev polynomials of the first kind ; Sums of finite products ; Orthogonal polynomials
