Serkan Araci

A Study on the Fermionic -Adic -Integral Representation on ℤ Associated with Weighted -Bernstein and -Genocchi Polynomials

We consider weighted 𝑞-Genocchi numbers and polynomials. We investigated some interesting properties of the weighted 𝑞-Genocchi numbers related to weighted 𝑞-Bernstein polynomials by using fermionic 𝑝-adic integrals on ℤ𝑝.

New Construction Weighted h, q -Genocchi Numbers and Polynomials Related to Zeta Type Functions

The fundamental aim of this paper is to construct -Genocchi numbers and polynomials with weight . We shall obtain some interesting relations by using -adic -integral on in the sense of fermionic. Also, we shall derive the -extensions of zeta type functions with weight from the Mellin transformation of this generating function which interpolates the -Genocchi numbers and polynomials with weight at negative integers.

Novel identities involving Genocchi numbers and polynomials arising from applications of umbral calculus

Abstract The aim of this paper is to deal with applications of umbral calculus on fermionic p -adic integral on Z p . From those applications, we derive some new identities on Genocchi numbers and polynomials. Moreover, a systemic study of the class of Sheffer sequences on the generating function of Genocchi polynomials are given.

A New Approach to q-Bernoulli Numbers and q-Bernoulli Polynomials Related to q-Bernstein Polynomials

We present a new generating function related to the -Bernoulli numbers and -Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and -Bernstein polynomials. We also consider the generalized -Bernoulli polynomials attached to Dirichlets character and have their generating function . We obtain distribution relations for the -Bernoulli polynomials and have some identities involving -Bernoulli numbers and polynomials related to the second kind Stirling numbers and -Bernstein polynomials. Finally, we derive the -extensions of zeta functions from the Mellin transformation of this generating function which interpolates the -Bernoulli polynomials at negative integers and is associated with -Bernstein polynomials.We present a new generating function related to the Open image in new window -Bernoulli numbers and Open image in new window -Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and Open image in new window -Bernstein polynomials. We also consider the generalized Open image in new window -Bernoulli polynomials attached to Dirichlets character Open image in new window and have their generating function . We obtain distribution relations for the Open image in new window -Bernoulli polynomials and have some identities involving Open image in new window -Bernoulli numbers and polynomials related to the second kind Stirling numbers and Open image in new window -Bernstein polynomials. Finally, we derive the Open image in new window -extensions of zeta functions from the Mellin transformation of this generating function which interpolates the Open image in new window -Bernoulli polynomials at negative integers and is associated with Open image in new window -Bernstein polynomials.

Explicit Formulas Involving -Euler Numbers and Polynomials

We deal with -Euler numbers and -Bernoulli numbers. We derive some interesting relations for -Euler numbers and polynomials by using their generating function and derivative operator. Also, we derive relations between the -Euler numbers and -Bernoulli numbers via the -adic -integral in the -adic integer ring.

Extended p -adic q -invariant integrals on Z p associated with applications of umbral calculus

The fundamental aim of this paper is to consider some applications of umbral calculus by utilizing from the extended p-adic q-invariant integral on Zp. From those considerations, we derive some new interesting properties on the extended p-adic q-Bernoulli numbers and polynomials. That is, a systemic study of the class of Sheffer sequences in connection with generating function of the p-adic q-Bernoulli polynomials are given in the present work.MSC:05A10, 11B65, 11B68, 11B73.

SOME NEW PROPERTIES ON THE q-GENOCCHI NUMBERS AND POLYNOMIALS ASSOCIATED WITH q-BERNSTEIN POLYNOMIALS

The purpose of this study is to obtain some relations between q-Genocchi numbers and q-Bernstein polynomials by using fermionic p-adic q-integral on Zp.

A note on the (h,q)-zeta-type function with weight α

The objective of this paper is to derive the symmetric property of an (h,q)-zeta function with weight α. By using this property, we give some interesting identities for (h,q)-Genocchi polynomials with weight α. As a result, our applications possess a number of interesting properties which we state in this paper.MSC:11S80, 11B68.The objective of this paper is to derive the symmetric property of an ( h , q ) Open image in new window-zeta function with weight α. By using this property, we give some interesting identities for ( h , q ) Open image in new window-Genocchi polynomials with weight α. As a result, our applications possess a number of interesting properties which we state in this paper.

A note on the modified q-Bernstein polynomials for functions of several variables and their reflections on q-Volkenborn integration

Abstract In this paper, we consider the modified q -Bernstein polynomials for functions of several variables on q -Volkenborn integral and investigate some new interesting properties of these polynomials related to q -Stirling numbers, Hermite polynomials and Carlitz’s type q -Bernoulli numbers.

New Symmetric Identities Involving q-Zeta Type Functions

The main object of this paper is to obtain several symmetric properties of the q-zeta type functions. As applications of these properties, we give some new interesting identities for the modified q-Genocchi polynomials. Finally, our applications are shown to lead to a number of interesting results which we state in the present paper.