Some identities on the generalized q -bernoulli, q -euler, and q -Genocchi polynomials

Mahmudov (2012, 2013) introduced and investigated some q-extensions of the q-Bernoulli polynomials β_n,q^αx,y of order α, the q-Euler polynomials ℰ_n,q^αx,y of order α, and the q-Genocchi polynomials n,qαx,y of order α. In this paper, we give some identities for β_n,q ^αx,y, n,qαx,y, and ℰ_n,q ^αx,y and the recurrence relations between these polynomials. This is an analogous result to the q-extension of the Srivastava-Pintér addition theorem in Mahmudov (2013).