Some new identities of Chebyshev polynomials and their applications

[摘要] In this paper, we use the properties of Chebyshev polynomials, elementary methods, and combinational techniques to study the computational problem of one kind of convolution sums involving second kind Chebyshev polynomials, and we give an exact computational method, which expresses the sums as second kind Chebyshev polynomials. As some applications of our results, we also obtain several new identities and congruences involving the second kind Chebyshev polynomials, Fibonacci numbers, and Lucas numbers.

[学科分类] 数学（综合）

[关键词] second kind Chebyshev polynomials;Fibonacci number;Lucas number;identity;11B39