Results 11 to 20 of about 96 (94)
Advances in Difference Equations, 2011 This paper performs a further investigation on the q-Bernoulli numbers and q-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010), some incorrect properties are revised.
Kim Taekyun, Lee Byungje, Ryoo Cheon
doaj +1 more source
Fourier series of higher-order Bernoulli functions and their applications. [PDF]
J Inequal Appl, 2017 In this paper, we study the Fourier series related to higher-order Bernoulli functions and give new identities for higher-order Bernoulli functions which are derived from the Fourier series of them.
Kim T, Kim DS, Rim SH, Dolgy DV.
europepmc +2 more sources
The homogenized Linial arrangement and Genocchi numbers [PDF]
, 2022 We study the intersection lattice of a hyperplane arrangement recently introduced by Hetyei who showed that the number of regions of the arrangement is a median Genocchi number.
Wachs, Michelle L., +3 more
core +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 12, Page 599-605, 2004., 2004 We consider the modified q‐analogue of Riemann zeta function which is defined by ζq(s)=∑n=1∞(qn(s−1)/[n]s), 0 < q < 1, s ∈ ℂ. In this paper, we give q‐Bernoulli numbers which can be viewed as interpolation of the above q‐analogue of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at ...
Taekyun Kim
wiley +1 more source
An extension of q‐zeta function
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 49, Page 2649-2651, 2004., 2004 We will define the extension of q‐Hurwitz zeta function due to Kim and Rim (2000) and study its properties. Finally, we lead to a useful new integral representation for the q‐zeta function.
T. Kim, L. C. Jang, S. H. Rim
wiley +1 more source
Generalizations of Bernoulli numbers and polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 59, Page 3769-3776, 2003., 2003 The concepts of Bernoulli numbers Bn, Bernoulli polynomials Bn(x), and the generalized Bernoulli numbers Bn(a, b) are generalized to the one Bn(x; a, b, c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between Bn, Bn(x), Bn(a, b), and Bn(
Qiu-Ming Luo +3 more
wiley +1 more source
Generalizations of Euler numbers and polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 61, Page 3893-3901, 2003., 2003 The concepts of Euler numbers and Euler polynomials are generalized and some basic properties are investigated.
Qiu-Ming Luo, Feng Qi, Lokenath Debnath
wiley +1 more source
Degenerate Hermite poly-Bernoulli numbers and polynomials with q-parameter
, 2020 In this paper, we introduce a new class of degenerate Hermite polyBernoulli polynomials with q-parameter and give some identities of these polynomials related to the Stirling numbers of the second kind.
KHAN, Idrees A. +2 more
core +1 more source
On modified degenerate Carlitz q-Bernoulli numbers and polynomials [PDF]
, 2017 In a recent study by Kim (Bull. Korean Math. Soc. 53(4):1149-1156, 2016 ) an attempt was made to examine some of the identities and properties that are related to the degenerate Carlitz q -Bernoulli numbers and polynomials.
Jeong Gon Lee +3 more
core +1 more source
Some convolution identities for Frobenius-Euler polynomials
, 2017 In this paper, by applying the generating function methods and summation transform techniques, we establish some new convolution identities for the Frobenius-Euler polynomials. It turns out that some well-known results are obtained as special cases.
Jing Pan +3 more
core +1 more source