Barnes' multiple Bernoulli and poly-Bernoulli mixed-type polynomials

TL;DR

This paper explores Barnes' multiple Bernoulli and poly-Bernoulli mixed-type polynomials, deriving new identities using Sheffer sequences and umbral calculus to deepen understanding of their properties.

Contribution

It introduces new identities for Barnes' multiple Bernoulli and poly-Bernoulli mixed-type polynomials via Sheffer sequences and umbral calculus.

Findings

Derived new identities for the polynomials.

Connected properties of Sheffer sequences with these polynomials.

Enhanced understanding of their algebraic structure.

Abstract

In this paper, we consider Barnes' multiple Bernoulli and poly-Bernoulli mixed-type polynomials. From the properties of Sheffer sequences of these polynomials arising from umbrral calculus, we derive new and interesting identities.