In this paper we study that the q-Euler numbers and polynomials are analytically continued to Eq(s). A new formula for the Euler’s q-Zeta function ζE,q(s) in terms of nested series of ζE,q(n) is derived. Finally we introduce the new concept of the dynamics of analytically continued q-Euler numbers and polynomials. 2000 Mathematics Subject Classification 11B68, 11S40 Key wordsq-Bernoulli polynom...

By using q-Volkenborn integration and uniform differentiable on Zp, we construct p-adic q-zeta functions. These functions interpolate the qBernoulli numbers and polynomials. The value of p-adic q-zeta functions at negative integers are given explicitly. We also define new generating functions of q-Bernoulli numbers and polynomials. By using these functions, we prove analytic continuation of som...

We introduce several q-differential equations of higher order which are related to q-Bernoulli polynomials and obtain a symmetric property in this paper. By giving q-varying variations, we identify the shape approximate roots polynomials, solution order, find conjectures associated with them. Furthermore, based on create Mandelbrot set Julia variety figures.

and reproduction in any medium, provided the original work is properly cited. Abstract. In this paper, we study some properties of Changhee's q-Bernou lli polynomials which are derived from p-adic invariant integral on Z p. By using these properties, we give some interesting identities related to higher-order q-Bernoulli polynomials.

In this paper, we expand functions of specific q-exponential growth in terms its even (odd) Askey-Wilson q-derivatives at 0 and η=(q1/4+q−1/4)/2. This expansion is a q-version the celebrated Lidstone theorem, where function q-analogs polynomials, i.e., q-Bernoulli q-Euler polynomials as classical case. We also raise solve q-extension problem representing an entire form f(z)=g(z+1)−g(z), g(z) sa...

the principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (iae) by using the bernoulli polynomials and the residual correction method. after implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown bernoulli coefficients. thismethod gives an analytic solution when t...

In this paper, we give some interesting symmetric identities of generalized higher-order Carlitz q-Bernoulli polynomials attached to χ which are derived from symmetry properties of multivariate p-adic q-integral on X.