Abstract

The main purpose of this paper is to introduce some generalizations of the Bernoulli-Barnes polynomials. These generalizations come from suitable modifications of the Mittag-Leffler type function linked to the generating function corresponding to the Bernoulli-Barnes polynomials. We provide several algebraic and combinatorial properties for these new classes of polynomials involving the Norlund polynomials, Frobenius-Euler functions and Stirling numbers of second kind. Also, we deduce some connection formulae between a subclass of generalized Apostol-type Bernoulli-Barnes polynomials and the Jacobi polynomials, generalized Bernoulli polynomials, Genocchi polynomials and Apostol-Euler polynomials, respectively.