Utilizing p,q-numbers and p,q-concepts, in 2016, Duran et al. considered p,q-Genocchi numbers polynomials, p,q-Bernoulli polynomials p,q-Euler provided multifarious formulas properties for these polynomials. Inspired motivated by this consideration, many authors have introduced (p,q)-special described some of their applications. In paper, using the (p,q)-cosine (p,q)-sine we consider a novel ki...

Abstract : The object of this paper is to give several properties and applications of the multiple p-adic q-L-function of two variables L (r) p,q (s, z, χ). The explicit formulas relating higher order qBernoulli polynomials, which involve sums of products of higher order q-zeta function and higher order Dirichlet q-L-function are given. The value of higher order Dirichlet p-adic q-L-function fo...

Keywords: Genocchi numbers and polynomials q-Genocchi numbers von Staudt–Clausen's theorem Kummer congruence a b s t r a c t Recently, the von Staudt–Clausen's theorem for q-Euler numbers was introduced by Kim (2013) and q-Genocchi numbers were constructed by Araci et al. (2013). In this paper, we give the corresponding von Staudt–Clausen's theorem for q-Genocchi numbers and also get the Kummer...

The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Z p. Finally, we will give some interesting formula related to these q-Euler numbers and polynomials. The usual Bernoulli numbers are defined by ∞ k=0 B k t k k! = t e t − 1 , which can be written symbolically as e Bt = t e t −1 , interpreted to mean B k must be replaced by B k when...

In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly de…ned (q; r; w)Stirling numbers of the second kind. We also obtain q-Bernstein polynomials as a linear combination of (q...

The aim of this paper is to construct new Dedekind type sums. We construct generating functions of Barnes’ type multiple FrobeniusEuler numbers and polynomials. By applying Mellin transformation to these functions, we define Barnes’ type multiple l-functions, which interpolate Frobenius-Euler numbers at negative integers. By using generalizations of the Frobenius-Euler functions, we define gene...

In this paper, we define the generating functions for the generalized q-Stirling numbers of the second kind. By applying Mellin transform to these functions, we construct interpolation functions of these numbers at negative integers. We also derive some identities and relations related to q-Bernoulli numbers and polynomials and q-Stirling numbers of the second kind.