Veli Kurt

New approach to the complete sum of products of the twisted (h, q)-Bernoulli numbers and polynomials

Abstract In this paper, by using q-Volkenborn integral[10], the first author[25] constructed new generating functions of the new twisted (h, q)-Bernoulli polynomials and numbers. We define higher-order twisted (h, q)-Bernoulli polynomials and numbers. Using these numbers and polynomials, we obtain new approach to the complete sums of products of twisted (h, q)-Bernoulli polynomials and numbers. p-adic q-Volkenborn integral is used to evaluate summations of the following form: where is the twisted (h, q)-Bernoulli polynomials. We also define new identities involving (h, q)-Bernoulli polnomials and numbers.

q-Genocchi Numbers and Polynomials Associated with q-Genocchi-Type l-Functions

The main purpose of this paper is to study on generating functions of the Open image in new window -Genocchi numbers and polynomials. We prove new relation for the generalized Open image in new window -Genocchi numbers which is related to the Open image in new window -Genocchi numbers and Open image in new window -Bernoulli numbers. By applying Mellin transformation and derivative operator to the generating functions, we define Open image in new window -Genocchi zeta and Open image in new window -functions, which are interpolated Open image in new window -Genocchi numbers and polynomials at negative integers. We also give some applications of generalized Open image in new window -Genocchi numbers.The main purpose of this paper is to study on generating functions of the -Genocchi numbers and polynomials. We prove new relation for the generalized -Genocchi numbers which is related to the -Genocchi numbers and -Bernoulli numbers. By applying Mellin transformation and derivative operator to the generating functions, we define -Genocchi zeta and -functions, which are interpolated -Genocchi numbers and polynomials at negative integers. We also give some applications of generalized -Genocchi numbers.

Multiple two-variable p-adic q-L-function and its behavior at s = 0

The objective of this paper is to construct a multiple p-adic q-L-function of two variables which interpolates multiple generalized q-Bernoulli polynomials. By using this function, we solve a question of Kim and Cho. We also define a multiple partial q-zeta function which is related to the multiple q-L-function of two variables. Finally, we give a finite-sum representation of the multiple p-adic q-L-function of two variables and prove a multiple q-extension of the generalized formula of Diamond and Ferrero-Greenberg.

Congruences for Generalized -Bernoulli Polynomials

In this paper, we give some further properties of -adic --function of two variables, which is recently constructed by Kim (2005) and Cenkci (2006). One of the applications of these properties yields general classes of congruences for generalized -Bernoulli polynomials, which are -extensions of the classes for generalized Bernoulli numbers and polynomials given by Fox (2000), Gunaratne (1995), and Young (1999, 2001).

Character analogues of certain Hardy-Berndt sums

In this paper we consider transformation formulas for \[ B\left( z,s:\chi\right) =\sum\limits_{m=1}^{\infty}\sum\limits_{n=0} ^{\infty}\chi(m)\chi(2n+1)\left( 2n+1\right) ^{s-1}e^{\pi im(2n+1)z/k}. \] We derive reciprocity theorems for the sums arising in these transformation formulas and investigate certain properties of them. With the help of the character analogues of the Euler--Maclaurin summation formula we establish integral representations for the Hardy-Berndt character sums

A NEW APPROACH TO q-GENOCCHI NUMBERS AND POLYNOMIALS

s_{3,p}\left( d,c:\chi\right)

New identities and relations derived from the generalized Bernoulli polynomials, Euler polynomials and Genocchi polynomials

and

Some Identities on the Generalized q-Bernoulli, q-Euler, and q-Genocchi Polynomials

s_{4,p}\left( d,c:\chi\right)

Some symmetry identities for the Apostol-type polynomials related to multiple alternating sums

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Chebyshev-type matrix polynomials and integral transforms

In this paper, new q-analogs of Genocchi numbers and poly- nomials are defined. Some important arithmetic and combinatoric rela- tions are given, in particular, connections with q-Bernoulli numbers and polynomials are obtained.