Some Explicit Formulas for the Generalized Frobenius-Euler Polynomials of Higher Order

Abstract

Our aim is to derive some explicit formulas for the generalized Bernoulli and Euler polynomials in terms of Whitney and translated Whitney numbers of the second kind. Also we derive some explicit formula for the generalized Euler  polynomials and Genocchi-like polynomials in terms of generalized Whitney polynomials of the second kind. We provide an algorithm for computing the generalized Frobenius-Euler polynomials of higher order.