Lucas-Euler relations using balancing and Lucas-balancing polynomials
Number Theory
2020-09-22 v1
Abstract
We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions. From these polynomial relations, we deduce interesting identities with Fibonacci and Lucas numbers, and Euler numbers. The results must be regarded as companion results to some Fibonacci-Bernoulli identities, which we derived in our previous paper.
Cite
@article{arxiv.2009.09409,
title = {Lucas-Euler relations using balancing and Lucas-balancing polynomials},
author = {Robert Frontczak and Taras Goy},
journal= {arXiv preprint arXiv:2009.09409},
year = {2020}
}
Comments
11 pages