The sums of the reciprocals of Fibonacci polynomials and Lucas polynomials

Abstract

In this article, we consider infinite sums derived from the reciprocals of the Fibonacci polynomials and Lucas polynomials, and infinite sums derived from the reciprocals of the square of the Fibonacci polynomials and Lucas polynomials. Then applying the floor function to these sums, we obtain several new equalities involving the Fibonacci polynomials and Lucas polynomials. © 2012 Zhengang and Wenpeng; licensee Springer.