Abstract.

The main purpose of this paper is to introduce (p; q)-Frobenius-Euler numbers and polynomials, and to investigate their some identities and properties including addition property, difference equation, derivative property, recurrence relationships. We also obtain integral representation, explicit formulae and relations for these polynomials and numbers. Furthermore, we consider some relationships for (p; q)-Frobenius-Euler polynomials of order  associated with (p; q)-Bernoulli polynomials, (p; q)-Euler polynomials and (p; q)-Genocchi polynomials.

Keywords:

(p; q)-Bernoulli polynomials, (p; q)-Euler polynomials, (p; q)-Genocchi polynomials, (p; q)-Frobenius-Euler polynomials, generating function, Cauchy product.