A class of identities satisfied by both Bernoulli and Euler polynomials is established. Recurrence relations for Bernoulli and Euler numbers are derived.

In a recent paper, Guo, Mező, and Qi proved an identity representing the Bernoulli polynomials at non-negative integer points m in terms of the m-Stirling numbers of the second kind. In this note, using a new representation of the Bernoulli polynomials in the context of the Zeon algebra, we give an alternative proof of the aforementioned identity.

This article presents a generalization of new classes degenerated Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi Hermite polynomials level m. We establish some algebraic differential properties for generalizations Apostol–Bernoulli polynomials. These results are shown using generating function methods Apostol–Euler