Open Access Research

The sums of the reciprocals of Fibonacci polynomials and Lucas polynomials

Zhengang Wu* and Wenpeng Zhang

Author Affiliations

Department of Mathematics, Northwest University, Xi'an, Shaanxi, P.R. China

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Journal of Inequalities and Applications 2012, 2012:134 doi:10.1186/1029-242X-2012-134

Published: 11 June 2012

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.

Mathematics Subject Classification (2010): Primary, 11B39.

Keywords:
Fibonacci polynomials; Lucas polynomials; inequality; floor function