Multifarious implicit summation formulae of Hermite-based poly-Daehee polynomials

Abstract

In this paper, we introduce the generating function of Hermite-based poly-Daehee numbers and polynomials. By making use of this generating function, we investigate some new and interesting identities for the Hermite-based poly-Daehee numbers and polynomials including recurrence relations, addition property and correlations with poly-Bernoulli polynomials of second kind. We then derive diverse implicit summation formula for Hermite-based poly-Daehee numbers and polynomials by applying the series manipulation methods.