Degenerate Versions of Hypergeometric Bernoulli–Euler Polynomials

Abstract

In this paper, we introduce degenerate versions of the hypergeometric Bernoulli and Euler polynomials. We demonstrate that they form $$\Delta_{\lambda}$$ –Appell sets and provide some of their algebraic properties, including inversion formulas, as well as the associated matrix formulation. Additionally, we focus our attention on the monomiality principle associated with them and determine the corresponding derivative and multiplicative operators.