Reciprocal Formulae among Pell and Lucas Polynomials

Abstract

Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions. Their special cases result in several interesting identities concerning Fibonacci and Lucas numbers.

Keywords

• generating function
• Lambert series
• bisection series
• reciprocal relation
• binomial coefficient
• Fibonacci and Lucas numbers