Abstract:
In this paper, we use the algebraic manipulations and
the properties of Chebyshev polynomials to obtain two interesting
identities involving the power sums of the integral of the first
kind Chebyshev polynomials, and partly solved an open problem
proposed by Xiaoxue Li in a paper published recently. As some
applications, we obtained some identities involving Fibonacci
numbers and Lucas numbers.
Key Words: The integral of the first kind
Chebyshev polynomials; power sums; Fibonacci number; Lucas number;
identity.
2010 Mathematics Subject Classification: 11B39
