Results 41 to 50 of about 56,955 (119)
Completeness of Ordered Fields and a Trio of Classical Series Tests
Abstract and Applied Analysis, Volume 2016, Issue 1, 2016., 2016 This article explores the fate of the infinite series tests of Dirichlet, Dedekind, and Abel in the context of an arbitrary ordered field. It is shown that each of these three tests characterizes the Dedekind completeness of an Archimedean ordered field; specifically, none of the three is valid in any proper subfield of R.
Robert Kantrowitz +2 more
wiley +1 more source
A new generalization of Apostol-type Laguerre–Genocchi polynomials
Comptes Rendus. Mathématique, 2017 Many extensions and variants of the so-called Apostol-type polynomials have recently been investigated. Motivated mainly by those works and their usefulness, we aim to introduce a new class of Apostol-type Laguerre–Genocchi polynomials associated with the modified Milne–Thomson's polynomials introduced by Derre and Simsek and investigate its properties,
Khan, Nabiullah +2 more
openaire +2 more sources
Relations for Bernoulli--Barnes Numbers and Barnes Zeta Functions
, 2013 The \emph{Barnes $\zeta$-function} is \[ \zeta_n (z, x; \a) := \sum_{\m \in \Z_{\ge 0}^n} \frac{1}{\left(x + m_1 a_1 + \dots + m_n a_n \right)^z} \] defined for $\Re(x) > 0$ and $\Re(z) > n$ and continued meromorphically to $\C$.
Bayad, Abdelmejid, Beck, Matthias
core +2 more sources
The multi-variable unified family of generalized Apostol-type polynomials
Applicable Analysis and Discrete Mathematics, 2020 The aim of this paper is to investigate and give a new family of multi-variable Apostol-type polynomials. This family is related to Apostol-Euler, Apostol-Bernoulli, Apostol-Genocchi and Apostol-laguerre polynomials.
S. B. El-Desouky, S. Gomaa, M. Magar
semanticscholar +1 more source
General‐Appell Polynomials within the Context of Monomiality Principle
International Journal of Analysis, Volume 2013, Issue 1, 2013., 2013 A general class of the 2‐variable polynomials is considered, and its properties are derived. Further, these polynomials are used to introduce the 2‐variable general‐Appell polynomials (2VgAP). The generating function for the 2VgAP is derived, and a correspondence between these polynomials and the Appell polynomials is established.
Subuhi Khan +2 more
wiley +1 more source
Series Representations at Special Values of Generalized Hurwitz‐Lerch Zeta Function
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 By making use of some explicit relationships between the Apostol‐Bernoulli, Apostol‐Euler, Apostol‐Genocchi, and Apostol‐Frobenius‐Euler polynomials of higher order and the generalized Hurwitz‐Lerch zeta function as well as a new expansion formula for the generalized Hurwitz‐Lerch zeta function obtained recently by Gaboury and Bayad , in this paper we ...
S. Gaboury, A. Bayad, Junesang Choi
wiley +1 more source
The Iwasawa invariants of Zpd${\mathbb {Z}}_{p}^{\,d}$‐covers of links
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract Let p$p$ be a prime number and let d∈Z>0$d\in {\mathbb {Z}}_{>0}$. In this paper, following the analogy between knots and primes, we study the p$p$‐torsion growth in a compatible system of (Z/pnZ)d$({\mathbb {Z}}/p^n{\mathbb {Z}})^d$‐covers of 3‐manifolds and establish several analogues of Cuoco–Monsky's multivariable versions of Iwasawa's ...
Sohei Tateno, Jun Ueki
wiley +1 more source
Old and New Identities for Bernoulli Polynomials via Fourier Series
International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 The Bernoulli polynomials Bk restricted to [0, 1) and extended by periodicity have nth sine and cosine Fourier coefficients of the form Ck/nk. In general, the Fourier coefficients of any polynomial restricted to [0, 1) are linear combinations of terms of the form 1/nk. If we can make this linear combination explicit for a specific family of polynomials,
Luis M. Navas +3 more
wiley +1 more source
Parametric kinds of generalized Apostol-Bernoulli polynomials and their properties
, 2023 The purpose of this paper is to define generalized Apostol--Bernoulli polynomials with including a new cosine and sine parametric type of generating function using the quasi-monomiality properties and trigonometric functions.
Kızılateş, Can +3 more
core
On the generalized Apostol-type Frobenius-Genocchi polynomials
Filomat, 2019 The main object of this work is to introduce a new class of the generalized Apostol-type Frobenius-Genocchi polynomials and is to investigate some properties and relations of them. We derive implicit summation formulae and symmetric identities by applying the generating functions.
Khan, Waseem A., Srivastava, Divesh
openaire +3 more sources