Additional Fibonacci-Bernoulli relations

TL;DR

This paper explores new relationships between Fibonacci, Lucas, and Bernoulli numbers and polynomials using generating functions involving hyperbolic functions, revealing interesting mathematical properties.

Contribution

It introduces novel Fibonacci-Bernoulli relations derived from functional equations of generating functions, expanding the understanding of their interconnectedness.

Findings

Derived new Fibonacci-Bernoulli identities

Analyzed special cases and corollaries

Highlighted interesting mathematical properties

Abstract

We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli numbers and polynomials. The derivations of our results are based on functional equations for the respective generating functions, which in our case are combinations of hyperbolic functions. Special cases and some corollaries will highlight interesting aspects of our findings.