A New Identity Involving the Chebyshev Polynomials

摘要

In this paper, firstly, we introduced a second order non-linear recursive sequence, then we use this sequence and the combinatorial methods to perform a deep study on the computational problem concerning one kind sums, which includes the Chebyshev polynomials. This makes it possible to simplify a class of complex computations involving the second type Chebyshev polynomials into a very simple problem. Finally, we give a new and interesting identity for it.