Hacer Ozden

A new extension of q-Euler numbers and polynomials related to their interpolation functions

Abstract In this work, by using a p -adic q -Volkenborn integral, we construct a new approach to generating functions of the ( h , q ) -Euler numbers and polynomials attached to a Dirichlet character χ . By applying the Mellin transformation and a derivative operator to these functions, we define ( h , q ) -extensions of zeta functions and l -functions, which interpolate ( h , q ) -extensions of Euler numbers at negative integers.

A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials

The goal of this paper is to unify and extend the generating functions of the generalized Bernoulli polynomials, the generalized Euler polynomials and the generalized Genocchi polynomials associated with the positive real parameters a and b and the complex parameter @b. By using this generating function, we derive recurrence relations and other properties for these polynomials. By applying the Mellin transformation to the generating function of the unification of Bernoulli, Euler and Genocchi polynomials, we construct a unification of the zeta functions. Furthermore, we give many properties and applications involving the functions and polynomials investigated in this paper.

Multivariate interpolation functions of higher-order -Euler numbers and their applications.

The aim of this paper, firstly, is to construct generating functions of 𝑞-Euler numbers and polynomials of higher order by applying the fermionic 𝑝-adic 𝑞-Volkenborn integral, secondly, to define multivariate 𝑞-Euler zeta function (Barnes-type Hurwitz 𝑞-Euler zeta function) and 𝑙-function which interpolate these numbers and polynomials at negative integers, respectively. We give relation between Barnes-type Hurwitz 𝑞-Euler zeta function and multivariate 𝑞-Euler 𝑙-function. Moreover, complete sums of products of these numbers and polynomials are found. We give some applications related to these numbers and functions as well.

Remarks on Sum of Products of -Twisted Euler Polynomials and Numbers

The main purpose of this paper is to construct generating functions of higher-order twisted -extension of Euler polynomials and numbers, by using -adic, -deformed fermionic integral on . By applying these generating functions, we prove complete sums of products of the twisted -extension of Euler polynomials and numbers. We also define some identities involving twisted -extension of Euler polynomials and numbers.

Modification and unification of the Apostol-type numbers and polynomials and their applications

Abstract In this paper, we construct generating functions for modification and unification of the Apostol-type polynomials Y n , β ( v ) ( x ; k , a , b ) of order v. By using these generating functions, we derive many new identities related to the generalized Stirling type numbers of the second kind, array-type polynomials, Eulerian polynomials and the modification and unification of the Apostol-type polynomials and numbers. We give many applications related to these numbers and polynomials and PDEs.

p-Adic distribution of the unification of the Bernoulli, Euler and Genocchi polynomials

Abstract The aim of this paper is to construct p-adic distribution, on X ⊂ C p , of the unification of the Bernoulli, Euler and Genocchi polynomials Y n , β ( x ; k , a , b ) , which is given by μ n , β , k , a , b j + dp N Z p = a b ( dp N - p ) ( dp N ) n - k β a jb Y n , β dp N j dp N , k , a dp N , b , where Y n , β ( x ; k , a , b ) are defined by (1.1) . We give some applications related to these functions and distribution.

A unified presentation of certain meromorphic functions related to the families of the partial zeta type functions and the L-functions

Abstract The aim of this paper is to construct a unified family of meromorphic functions, which is related to many known functions such as a unified family of partial zeta type functions, a unified family of L -functions, and so on. We investigate and derive many properties of this family of meromorphic functions. Moreover, we compute the residues of this family of meromorphic functions at their poles. We also give some applications and remarks involving this family of meromorphic functions.

Hurwitz Type Multiple Genocchi Zeta Function

Main purpose of this paper is to construct higher‐order w‐q‐Genocchi numbers and polynomials by using p‐adic q‐deformed fermionic integral on Zp. We derive some interesting identities related to higher‐order w‐q‐Genocchi numbers and polynomials. We also construct Hurwitz type multiple w‐Genocchi zeta function which interpolates these polynomials at negative integers.

Unified representation of the family of L -functions

The aim of this paper is to unify the family of L-functions. By using the generating functions of the Bernoulli, Euler and Genocchi polynomials, we construct unification of the L-functions. We also derive new identities related to these functions. We also investigate fundamental properties of these functions.AMS Subject Classification:11B68, 11S40, 11S80, 26C05, 30B40.

Generalized q-Stirling Numbers and Their Interpolation Functions

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.