Extended p-adic q-invariant integrals on "Equation missing" associated with applications of umbral calculus

The fundamental aim of this paper is to consider some applications of umbral calculus by utilizing from the extended p-adic q-invariant integral on Z p . From those considerations, we derive some new interesting properties on the extended p-adic q-Bernoulli numbers and polynomials. That is, a systemic study of the class of Sheffer sequences in connection with generating function of the p-adic q-Bernoulli polynomials are given in the present work. MSC:05A10, 11B65, 11B68, 11B73.