A Generalization of Power and Alternating Power Sums to Any Appell Polynomials

Abstract

In this paper, we will introduce Barnes' multiple Bernoulli and Appell mixed-type
polynomials, and Barnes' multiple Euler and Appell mixed-type polynomials.

Then we will establish one main identity for each of them connecting a sum for the
Appell polynomial and that for the mixed-type polynomial. As a consequence, the
direct generalization of the identities in (1.10) and (1.11) will follow from these as
special simple cases.