A note on Hermite-based truncated Euler polynomials

Abstract

In this paper, we introduce a new class of truncated Hermite-Euler polynomials and numbers as a generalization of Hermite-Euler polynomials. Furthermore, the discussion is on properties and relations with the hypergeometric Bernoulli polynomials, Frobenius-Euler polynomials and Stirling numbers of the second kind. As a result, we derive some implicit summation formulas of this polynomials.