2-Iterated Appell polynomials and related numbers

This article deals with the introduction of Appell type sets of polynomials and associated numbers. The 2-iterated Appell polynomials are introduced and the Bernoulli and Euler based Appell polynomials are deduced as their particular cases. Different sets of polynomials, namely 2-iterated Bernoulli and Euler, Bernoulli–Euler (or Euler–Bernoulli) and their related numbers are considered. The operational relations between these families and Appell polynomials are used on the results of the Bernoulli and Euler polynomials to obtain the results for the corresponding mixed polynomials.