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Related papers: A new class of generalized Genocchi polynomials

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In the present paper, we analyse analytic continuation of weighted q-Genocchi numbers and polynomials. A novel formula for weighted q-Genocchi- Zeta function {\zeta}G,q (s | {\alpha}) in terms of nested series of {\zeta}G,q (n | {\alpha})…

Number Theory · Mathematics 2013-08-14 Serkan Araci , Mehmet Acikgoz , Aynur Gursul

A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number--theoretical properties. A new class of…

Number Theory · Mathematics 2021-12-16 Piergiulio Tempesta

The main object of this paper is to construct a new generating function of the (q-) Bernstein type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and…

Number Theory · Mathematics 2018-11-19 Yilmaz Simsek , Mehmet Acikgoz

The q-binomial coefficients are the polynomial cousins of the traditional binomial coefficients, and a number of identities for binomial coefficients can be translated into this polynomial setting. For instance, the familiar vanishing of…

Number Theory · Mathematics 2012-02-02 Andrew Schultz , Robert Walker

Using sequences of finite length with positive integer elements and the inversion statistic on such sequences, a collection of binomial and multinomial identities are extended to their $q$-analog form via combinatorial proofs. Using the…

Combinatorics · Mathematics 2020-05-18 Adrian Avalos , Mark Bly

We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…

Number Theory · Mathematics 2016-01-19 Eric Y. Chen , J. T. Ferrara , Liam Mazurowski

This note is devoted to establish some new arithmetic properties of the generalized Genocchi numbers $G_{n , a}$ ($n \in \mathbb{N}$, $a \geq 2$). The resulting properties for the usual Genocchi numbers $G_n = G_{n , 2}$ are then derived.…

Number Theory · Mathematics 2021-03-16 Bakir Farhi

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…

Classical Analysis and ODEs · Mathematics 2015-07-07 Ana F. Loureiro , Jiang Zeng

In this paper, we study some properties of the q-Appell polynomials, including the recurrence relations and the q-difference equations which extend some known calssical (q=1) results. We also provide the recurrence relations and the…

Classical Analysis and ODEs · Mathematics 2014-03-04 Nazim I. Mahmudov

In the present paper, we deal with multiple generalized Genocchi numbers and polynomials. Also, we introduce analytic interpolating function for the multiple generalized Genocchi numbers attached to \c{hi} at negative integers in complex…

Number Theory · Mathematics 2013-09-23 Serkan Araci , Mehmet Acikgoz , Erdoğan Şen

In the present paper, the fundamental aim is to consider a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order modified Dedekind-type sums related to q-Genocchi polynomials with weight alpha by…

General Mathematics · Mathematics 2013-10-03 Serkan Araci , Erdoğan Şen , Mehmet Acikgoz

In this paper, we establish an identity for Bernoulli's generalized polynomials. We deduce generalizations for many relations involving classical Bernoulli numbers or polynomials. In particular, we generalize a recent Gessel identity.

Number Theory · Mathematics 2020-01-28 Redha Chellal , Farid Bencherif , Mohamed Mehbali

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…

Number Theory · Mathematics 2013-12-06 Mehmet Acikgoz , Serkan Araci

The focus of this paper is the study of generalized Fibonacci polynomials and Fibonomial coefficients. The former are polynomials {n} in variables s and t given by {0} = 0, {1} = 1, and {n} = s{n-1}+t{n-2} for n ge 2. The latter are defined…

Combinatorics · Mathematics 2013-07-30 Tewodros Amdeberhan , Xi Chen , Victor H. Moll , Bruce E. Sagan

In this paper, we give new identities involving Phillips q-Bernstein polynomials and we derive some interesting properties of q-Berstein polynomials associated with q-Stirling numbers and q-Bernoulli polynomials.

Number Theory · Mathematics 2010-08-27 T. Kim

In \cite{luo2006,luosri2005}, Luo and Srivastava introduced some generalizations of the Apostol -Bernoulli polynomials and the Apostol-Euler polynomials. The main object of this paper is to extend the result of \cite{prevost2010} to these…

Number Theory · Mathematics 2017-09-19 Marc Prévost

The purpose of this paper is to derive some identities of the higher order generalized twisted Bernoulli numbers and polynomials attached to $\chi$ from the properties of the p-adic invariant integrals.

Number Theory · Mathematics 2009-07-20 Younghee Kim , Seog-Hoon Rim , Byungje Lee , Taekyun Kim

The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.

Number Theory · Mathematics 2009-12-31 Taekyun Kim

In this paper, we introduce a new analogue of Lorentz polynomials based on (p,q)-integers and we call it as (p,q)-Lorentz polynomials. We obtain quantitative estimate in the Voronovskaja's type thoerem and exact orders in simultaneous…

Classical Analysis and ODEs · Mathematics 2015-04-21 M. Mursaleen , Faisal Khan , Asif Khan

In the present paper, our objective is to treat 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 in connection with modified q-Genocchi polynomials with weight…

Number Theory · Mathematics 2013-01-30 Serkan Araci , Mehmet Acikgoz , Ayhan Esi