相关论文: $q$-Volkenborn Integration and Its Applications
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming Y is a random variable satisfying moment conditions, we use the generating function of these…
In ths paper we discuss the new concept of the q-extension of Genocchi numbers and give the some relations between q-Genocchi polynomials and q-Euler numbers.
The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived. The $q$-analogue of the Srivastava--Pint\'er addition…
The purpose of this paper is to construct p-adic analytically continued function which interpolates q-Euler numbers at negative integer Finally, we give an explicit p-adic expansion as a power series in n.
The purpose of this paper is to construct of the unification q-extension Genocchi polynomials. We give some interesting relations of this type of polynomials. Finally, we derive the q-extensions of Hurwitz-zeta type functions from the…
The aim of this paper is to construct generating functions for some families of special finite sums with the aid of the Newton-Mercator series, hypergeometric series, and $p$-adic integral (the Volkenborn integral). By using these…
In this paper, we will constructed p-adic twisted q-l-functions which is a part of answer of the question in [8]. Finally, we will treat many interesting properties related to twisted q-Euler numbers and polynomials.
In this paper we consider the Witt's fprmula related to Carlitz's type q-Euler numbers and polynomials.
In this paper, we prove new identities for Bernoulli polynomials that extend Alzer and Kwong's results. The key idea is to use the Volkenborn integral over $\mathbb Z_p$ of the Bernoulli polynomials to establish recurrence relations on the…
The purpose of this paper concerns to establish modified q-Genocchi numbers and polynomials with weight ({\alpha},{\beta}). In this paper we investigate special generalized q-Genocchi polynomials and we apply the method of generating…
In this Ph.D. dissertation (2018, Emory University) we prove theorems at the intersection of the additive and multiplicative branches of number theory, bringing together ideas from partition theory, $q$-series, algebra, modular forms and…
In the present paper, we introduce Eulerian polynomials with a and b parameters and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Theory of Analytic…
By using q-Volkenborn integral on Z_{p}, we (simsek, simsekCanada) constructed new generating functions of the (h,q)-Bernoulli polynomials and numbers. By applying the Mellin transformation to the generating functions, we constructed…
The first aim of this paper is to construct new generating functions for the generalized {\lambda}-Stirling type numbers of the second kind, generalized array type polynomials and generalized Eulerian type polynomials and numbers, attached…
In this paper we give some interesting identities between Euler numbers and zeta functions. Finally we will give the new values of Euler zeta function at positive even integers.
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…
In this paper we construct $q$-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the $q$-analogue of alternating sums of powers of consecutive integers due to Euler.
In the present paper, our goal is to introduce a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order dedekind-type sums with weight alpha related to Extended q-Euler polynomials by using p-adic…