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

Veli Kurt, Burak Kurt

Mahmudov in ([16--18]) introduced and investigated some $q$-extensions of the $q$-Bernoulli polynomials $B^{(\alpha)}_{n,q}(x,y)$ of order $\alpha$, the $q$-Euler polynomials $\mathcal E^{(\alpha)}_{n,q}(x,y)$ of order $\alpha$ and the $q$-Genocchi polynomials $G^{(\alpha)}_{n,q}(x,y)$ of order $\alpha$. 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.