Some Identities and Recurrence Relations on the Two Variables Bernoulli, Euler and Genocchi Polynomials

Abstract

Mahmudov in (16, 17, 18) introduced and investigated some q-extensions of the q-Bernoulli polynomials B_{n,q}^{(α)}(x,y) of order α, the q-Euler polynomials E_{n,q}^{(α)}(x,y) of order α and the q-Genocchi polynomials G_{n,q}^{(α)}(x,y) of order α. In this article, we give some identities for the q-Bernoulli polynomials, q-Euler polynomials and q-Genocchi polynomials and the recurrence relation between these polynomials. We give a different form of the analogue of the Srivastava-Pintér addition theorem.