On hypergeometric Bernoulli numbers and polynomials

TL;DR

This paper explores properties of hypergeometric Bernoulli numbers and polynomials, including identities, differential equations, and recurrence relations, expanding understanding of their mathematical structure.

Contribution

It introduces new identities, differential equations, and recurrence formulas for hypergeometric Bernoulli numbers and polynomials, enhancing theoretical knowledge.

Findings

Derived sums of products identities

Established differential equations

Formulated recurrence relations

Abstract

In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.