Abstract. In [18], the new q-extension of Bernoulli polynomials and generalized Bernoulli numbers attached to χ were constructed by using p-adic invariant integral on Zp. In this paper we construct the new q-extension of generalized Bernoulli polynomials attached to χ due to author and derive the existence of a specific p-adic interpolation function which interpolate the q-extension of generali...

Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric properties, have been studied in the literature with help generating functions their functional equations. In this paper, we define generalized (p,q)-Bernoulli–Fibonacci (p,q)-Bernoulli–Lucas polynomials numbers by using (p,q)-Bernoulli numbers, unified h(x)-Fibonacci h(x)-Lucas polynomials. We als...

In this study, we construct the two-variable Dirichlet q-L-function and the two-variable multiple Dirichlet-type Changhee q-L-function. These functions interpolate the q-Bernoulli polynomials and generalized Changhee q-Bernoulli polynomials. By using the Mellin transformation, we give an integral representation for the two-variable multiple Dirichlet-type Changhee q-L-function. We also obtain r...

In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers and q-Bernoulli numbers and polynomials are deduced.

By using q-integration, we will give some integral equation which are related to the Barnes’ multiple Bernoulli numbers. The object of this paper is to give explicit q-integral’s formulae which are related to Barnes’ multiple q-Bernoulli polynomials. §

The main purpose of this paper is to consider q-sine-based and q-cosine-Based q-Fubini polynomials investigate diverse properties these polynomials. Furthermore, multifarious correlations including q-analogues the Genocchi, Euler Bernoulli polynomials, q-Stirling numbers second kind are derived. Moreover, some approximate zeros q-sinebased in a complex plane examined, lastly, shown using figures.