<it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisited

<it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisited

<p>Abstract</p> <p>This paper performs a further investigation on the <it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010), some incorrect properties are revised. It i...

Full description

Bibliographic Details
Main Authors:	Kim Taekyun, Lee Byungje, Ryoo Cheon
Format:	Article
Language:	English
Published:	SpringerOpen 2011-01-01
Series:	Advances in Difference Equations
Subjects:	Bernoulli numbers and polynomials <it>q</it>-Bernoulli numbers and polynomials
Online Access:	http://www.advancesindifferenceequations.com/content/2011/1/33

Similar Items

Some Identities for Euler and Bernoulli Polynomials and Their Zeros
by: Taekyun Kim, et al.
Published: (2018-08-01)

On p-adic Integral Representation of q-Bernoulli Numbers Arising from Two Variable q-Bernstein Polynomials
by: Dae San Kim, et al.
Published: (2018-10-01)

On Generating Functions for Parametrically Generalized Polynomials Involving Combinatorial, Bernoulli and Euler Polynomials and Numbers
by: Abdelmejid Bayad, et al.
Published: (2022-03-01)

Various Structures of the Roots and Explicit Properties of <i>q</i>-cosine Bernoulli Polynomials and <i>q</i>-sine Bernoulli Polynomials
by: Jung Yoog Kang, et al.
Published: (2020-03-01)

p-Adic integral on Z p $\mathbb{Z}_{p}$ associated with degenerate Bernoulli polynomials of the second kind
by: Lee-Chae Jang, et al.
Published: (2020-06-01)

Novel Identities of Bernoulli Polynomials Involving Closed Forms for Some Definite Integrals
by: Waleed Mohamed Abd-Elhameed, et al.
Published: (2022-10-01)

Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials
by: Dionisio Peralta, et al.
Published: (2023-09-01)

Identities and recurrence relations of special numbers and polynomials of higher order by analysis of their generating functions
by: Yilmaz Simsek, et al.
Published: (2018-08-01)

Expressions of Legendre polynomials through Bernoulli polynomials
by: Vu Kim Tuan, et al.
Published: (2011-01-01)

A parametric type of Bernoulli polynomials with higher level
by: T. Komatsu
Published: (2022-07-01)

Some new identities on the twisted carlitz's <b> <it>q</it> </b>-bernoulli numbers and <b> <it>q</it> </b>-bernstein polynomials
by: Kim Taekyun, et al.
Published: (2011-01-01)

Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character <i>χ</i>
by: Serkan Araci, et al.
Published: (2018-11-01)

Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials
by: Feng Qi, et al.
Published: (2016-11-01)

On Gould–Hopper-Based Fully Degenerate Poly-Bernoulli Polynomials with a <i>q</i>-Parameter
by: Ugur Duran, et al.
Published: (2019-01-01)

Fractional Bernoulli and Euler Numbers and Related Fractional Polynomials—A Symmetry in Number Theory
by: Diego Caratelli, et al.
Published: (2023-10-01)

On Generalized Bivariate (<i>p</i>,<i>q</i>)-Bernoulli–Fibonacci Polynomials and Generalized Bivariate (<i>p</i>,<i>q</i>)-Bernoulli–Lucas Polynomials
by: Hao Guan, et al.
Published: (2023-04-01)

A Note on Parametric Kinds of the Degenerate Poly-Bernoulli and Poly-Genocchi Polynomials
by: Taekyun Kim, et al.
Published: (2020-04-01)

Lagrange-Based Hypergeometric Bernoulli Polynomials
by: Sahar Albosaily, et al.
Published: (2022-05-01)

On Two Bivariate Kinds of Poly-Bernoulli and Poly-Genocchi Polynomials
by: Cheon Seoung Ryoo, et al.
Published: (2020-03-01)

A new class of generalized polynomials associated with Hermite and Bernoulli polynomials
by: M. A. Pathan, et al.
Published: (2015-05-01)

Note on Type 2 Degenerate <i>q</i>-Bernoulli Polynomials
by: Dae San Kim, et al.
Published: (2019-07-01)

Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials
by: Taekyun Kim, et al.
Published: (2020-04-01)

Some identities on the weighted q-Euler numbers and <it>q</it>-Bernstein polynomials
by: Ryoo Cheon, et al.
Published: (2011-01-01)

Fully degenerate Bernoulli numbers and polynomials
by: Kim Taekyun, et al.
Published: (2022-09-01)

Shifted sums of the Bernoulli numbers, reciprocity, and denominators
by: Bernd C. Kellner
Published: (2022-02-01)

Convolutions for Bernoulli and Euler–Genocchi Polynomials of Order (<i>r</i>,<i>m</i>) and Their Probabilistic Interpretation
by: Robert Frontczak, et al.
Published: (2022-06-01)

Fungsi Zeta Riemann Genap Menggunakan Bilangan Bernoulli
by: Ikhsan Maulidi, et al.
Published: (2019-02-01)

Fourier expansions for higher-order Apostol–Genocchi, Apostol–Bernoulli and Apostol–Euler polynomials
by: Cristina B. Corcino, et al.
Published: (2020-07-01)

On the apostol-bernoulli polynomials
by: Luo Qiu-Ming
Published: (2004-08-01)

Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials
by: Paolo Emilio Ricci, et al.
Published: (2024-01-01)

A Note on degenerate Euler and Bernoulli Polynomials of Complex Variable
by: Dae San Kim, et al.
Published: (2019-09-01)

New results on the q-generalized Bernoulli polynomials of level m
by: Urieles Alejandro, et al.
Published: (2019-12-01)

Degenerate Fubini-Type Polynomials and Numbers, Degenerate Apostol–Bernoulli Polynomials and Numbers, and Degenerate Apostol–Euler Polynomials and Numbers
by: Siqintuya Jin, et al.
Published: (2022-09-01)

A Parametric Kind of Fubini Polynomials of a Complex Variable
by: Sunil Kumar Sharma, et al.
Published: (2020-04-01)

Bell-Based Bernoulli Polynomials with Applications
by: Ugur Duran, et al.
Published: (2021-03-01)

Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials
by: Dmitry V. Dolgy, et al.
Published: (2019-07-01)

A new approach to Bernoulli polynomials
by: F. Costabile
Published: (2007-01-01)

A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials
by: Ghulam Muhiuddin, et al.
Published: (2021-04-01)

Degenerate poly-Bernoulli polynomials arising from degenerate polylogarithm
by: Taekyun Kim, et al.
Published: (2020-08-01)

Fourier Series for the Tangent Polynomials, Tangent–Bernoulli and Tangent–Genocchi Polynomials of Higher Order
by: Cristina Bordaje Corcino, et al.
Published: (2022-02-01)