Some identities involving Chebyshev polynomials, Fibonacci numbers and Lucas numbers

Abstract

In this paper we prove some identities involving Chebyshev polynomials, Fibonacci and Lucas numbers.

Identities for Fibonacci and Lucas numbers

“…Fibonacci numbers were studied in ancient and medieval India circa A.D. 600, [7]. Fibonacci and Lucas numbers [1][2][3][4][5] are also closely related to binomial coefficients. A study of Pascal's triangle reveals many patterns that are related to such numbers, including the identity…”

“…In [1,4] results were given for Fibonacci numbers in terms of binomial coefficients. In [2] identities with Fibonacci and Lucas numbers in terms of sums of binomial coefficients were also given.…”