A systemic study of some familier of the modified q-Euler numbers and polynomials with weight α is presented by using the p-adic qintergralon Zp.The study of these numbers and polynomials yields an interesting q-analoque related to Bernoulli numbers and polynomials. Mathematics Subject Classification: 05A30, 11B68, 11S80, 32P05

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we investigate some symmetric properties of p-adic q-integral on Z p. A question was asked in [10] as to finding formulae of symmetries for the generalized Ca...

We introduce $q$-analogues of the hypergeometric Bernoulli polynomials in one and two real parameters study several their properties. Also we provide inversion, power representation, multiplication addition formula for these polynomials. Classical results are recovered by limit transition.

We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).

We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).

and Applied Analysis 3 Similarly, the q-Bernoulli polynomials and numbers with weight 0 are defined, respectively, as B̃n,q x lim n→∞ 1 [ pn ] q pn−1 ∑ y 0 ( x y )n q

In this paper, we give new generating functions which produce Barnes' type multiple generalized Changhee q-Bernoulli polynomials and poly-nomials. These functions are very important to construct multiple zeta functions. By using Mellin transform's formula and Cauchy Theorem , we prove the analytic continuation of Barnes' type multiple Changhee q-zeta function. Finally we give some relations bet...

Motivated by Kurt’s work [Filomat 30 (4) 921-927, 2016], we …rst consider a class of a new generating function for (p; q)-analog of Apostol type polynomials of order including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order . By making use of their generating function, we derive some useful identities. We also introduce (p; q)-analog of Stirling numbers of second kind...