q−extensions for the U−Bernoulli and U−Euler polynomials

Abstract

This paper defines the q−U−Bernoulli, q − U−Euler polynomials and numbers and obtains some of their feature relations. We also explore the q − U−Bernoulli polynomials Ms (γ, q), Rogers-Szegö polynomials Hs (γ, q) and the q−Bernoulli numbers Bs (q) are related via some connection formulas. Further, we define various properties for the q−extensions U−Bernoulli and U−Euler polynomials like generating functions, q−partial derivatives and summation relations.