Some Identities on the Generalized q-Bernoulli, q-Euler, and q-Genocchi Polynomials

Abstract

Mahmudov (2012, 2013) introduced and investigated some q-extensions of the q-Bernoulli polynomials ℬn,qαx,y of order α, the q-Euler polynomials ℰn,qαx,y of order α, and the q-Genocchi polynomials 𝒢n,qαx,y of order α. In this paper, we give some identities for ℬn,qαx,y, 𝒢n,qαx,y, and ℰn,qαx,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).