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Related papers: A new class of generalized Genocchi polynomials

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In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.

Number Theory · Mathematics 2009-10-15 Kyoung-Ho Park , Young-Hee Kim , Taekyun Kim

Sequences of Genocchi numbers of the first and second kind are considered. For these numbers, an approach based on their representation using sequences of polynomials is developed. Based on this approach, for these numbers some identities…

Combinatorics · Mathematics 2019-11-26 Andrei K. Svinin

In this paper, some formulae for Genoochi polynomials of higher order are derived using the fact that sets of Bernoulli and Euler polynomials of higher order form basis for the polynomial space.

Classical Analysis and ODEs · Mathematics 2020-09-09 Cristina B. Corcino , Roberto B. Corcino , Joy Ann A. Canete

In this paper we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers and w-Genocchi numbers and polynomials of high order using the multivariate fermionic p-adic integral on Zp. We have the interpolation…

Number Theory · Mathematics 2009-01-14 Taekyun Kim , Young-hee Kim , Kyoung-won Hwang

The main objective of this paper is to introduce the modified q-Genocchi polynomials and to define their generating function. In the paper, we show new relations, which are explicit formula, derivative formula, multiplication formula, and…

Number Theory · Mathematics 2013-11-26 Serkan Araci , Armen Bagdasaryan , Erkan Agyuz , Mehmet Acikgoz

The rapid development of q-calculus has led to the discovery of new generalizations of Bernstein polynomials and Genocchi polynomials involving q-integers. The present paper deals with weighted q-Bernstein polynomials and q-Genocchi numbers…

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz

In this paper we give some interesting equation of p-adic q-integrals on Zp. From those p-adic q-integrals, we present a systemic study of some families of extended Carlitz q-Bernoulli numbers and polynomials in p-adic number field.

Number Theory · Mathematics 2010-08-10 T. Kim , Byungje Lee , C. S. Ryoo

In this paper, we will deal with some new formulae for two product Genocchi polynomials together with both Euler polynomials and Bernoulli polynomials. We get some applications for Genocchi polynomials. Our applications possess a number of…

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz , Erdoğan Şen

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…

Number Theory · Mathematics 2012-10-23 Serkan Araci , Mehmet Açikgöz , Hassan Jolany , Jong Jin Seo

The present paper deals with multiplication formulas for the Apostol-Genocchi polynomials of higher order and deduces some explicit recursive formulas. Some earlier results of Carlitz and Howard in terms of Genocchi numbers can be deduced.…

Number Theory · Mathematics 2012-10-23 Hassan Jolany , Hesam Sharifi

A new $q$-analog of Genocchi numbers is introduced through a q-analog of Seidel's triangle associated to Genocchi numbers. It is then shown that these $q$-Genocchi numbers have interesting combinatorial interpretations in the classical…

Combinatorics · Mathematics 2007-05-23 Jiang Zeng , Jin Zhou

We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.

History and Overview · Mathematics 2011-04-15 Johann Cigler

In this paper, we introduce a general family of $q$-hypergeometric polynomials and investigate several $q$-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family…

Combinatorics · Mathematics 2021-05-25 Hari Mohan Srivastava , Sama Arjika

By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.

Number Theory · Mathematics 2015-06-26 Taekyun Kim

In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.

Number Theory · Mathematics 2015-05-19 Taekyun Kim

In this paper, the authors deal with the $q$-Genocchi numbers and polynomials with weight zero. They discover some interesting relations via the $p$-adic $q$-integral on $\mathbb{Z}_{p}$ and familiar basis Bernstein polynomials. Finally,…

Number Theory · Mathematics 2013-08-05 Serkan Araci , Mehmet Acikgoz , Feng Qi

We introduce the generalized degenerate Euler-Genocchi polynomials as a degenerate version of the Euler-Genocchi polynomials. In addition, we introduce their higher-order version, namely the generalized degenerate Euler-Genocchi polynomials…

Number Theory · Mathematics 2022-08-24 Taekyun Kim , Dae San Kim , Hye Kyung Kim

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…

Classical Analysis and ODEs · Mathematics 2025-04-01 Ayse Karagenc , Mehmet Acikgoz , Serkan Araci

Recently, introduced are the generalized Euler-Genocchi and generalized degenerate Euler-Genocchi polynomials. The aim of this note is to study the multi-Euler-Genocchi and degenerate multi-Euler-Genocchi polynomials which are defined by…

Number Theory · Mathematics 2023-01-18 Taekyun Kim , Dae San Kim , Jin-Woo park , Jongkyum Kwon

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…

Combinatorics · Mathematics 2014-03-10 Serkan Araci , Mehmet Açikgöz , Feng Qi , Hassan Jolany