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.

Fibonacci Sums Modulo 5

“…There exists a countless number of binomial sums involving Fibonacci and Lucas numbers. For some new articles in this field we refer to the papers [1,5,2,6].…”