On some series representations of the Hurwitz zeta function
, 2008 A variety of infinite series representations for the Hurwitz zeta function are obtained. Particular cases recover known results, while others are new. Specialization of the series representations apply to the Riemann zeta function, leading to additional ...
Coffey, Mark W.
core +1 more source
COMPLETE ASYMPTOTIC EXPANSIONS FOR THE TRANSFORMED LERCH ZETA-FUNCTIONS VIA THE LAPLACE-MELLIN AND RIEMANN-LIOUVILLE OPERATORS (PRE-ANNOUNCEMENT) (Problems and prospects in Analytic Number Theory) [PDF]
, 2021 This is a pre-announcement version of the forthcoming paper [Complete asymptotic expansions for the transformed Lerch zeta-functions via the LaplaceMellin and Riemann-Liouville operators, preprint.].
KATSURADA, MASANORI
core
New Classes of Degenerate Unified Polynomials [PDF]
, 2022 In this paper, we introduce a class of new classes of degenerate unified polynomials and we show some algebraic and differential properties. This class includes the Appell-type classical polynomials and their most relevant generalizations.
Daniel Bedoya +7 more
core +1 more source
Extended Blumberg-Dieckmann Series
, 2023 This paper introduces a set of finite summation formulas and utilize them to establish various functional relationships involving the multivariable Hurwitz-Lerch zeta function.
Reynolds, Robert
core
An explicit expression of the Lerch zeta function on maximal domains of holomorphy
, 2023 We give two results on the Lerch zeta function $\Phi(z,\,s,\,w)$. The first is to give an explicit expression providing both the analytic continuation of $\Phi$ in $n$-variables $(n \in \{1,\,2,\,3\})$ to maximal domains of holomorphy in $\mathbb{C}^n ...
Kozuma, Rintaro
core
ASYMPTOTICS FOR HIGHER DERIVATIVES OF THE LERCH ZETA-FUNCTION: APPLICATIONS TO THE FORMULAE OF KUMMER, LERCH AND GAUSS (Analytic Number Theory and Related Topics) [PDF]
, 2019 Let s be a complex variables, z a complex parameter, and a and λ real parameters with a > 0, and write e(s) = e2πis. The Lerch zeta-function φ(s, a, λ) is defined by the Dirichlet series Σ∞ l=0 e(λl)(a + l)−s (Res > 1), and its meromorphic continuation ...
KATSURADA, MASANORI
core
Certain Extension of the Hurwitz-Lerch Zeta Function and its Properties
, 2020 يهدف هذا البحث إلى تقديم تمديد جديد لدالة هورويتز–ليرتش زيتا باستخدام تمديد بيتا المعرف في [1]. كما تم اثبات بعض الصيغ المعاودة، الدوال المولدة والتمثيلات التكاملية لذلك التمديد.The main object of this paper is to introduce a new extension of Hurwitz ...
Al-Gonah, Ahmed Ali +1 more
core
Extended Levett trigonometric series
, 2023 An extension of two finite trigonometric series is studied to derive closed form formulae involving the Hurwitz-Lerch zeta function. The trigonometric series involves angles with a geometric series involving the powers of 3.
Reynolds, Robert
core
A new class of degenerate Apostol-type Hermite polynomials and applications
, 2022 In this article, a new class of the degenerate Apostol–type Hermite polynomials is introduced. Certain algebraic and differential properties of there polynomials are derived.
Ramírez, William +2 more
core +1 more source
The Herglotz–Zagier function, double zeta functions, and values of L-series
, 2004 In this paper, we define L-series generalizing the Herglotz–Zagier function (Ber. Verhandl. Sächsischen Akad. Wiss. Leipzig 75 (3–14) (1923) 31, Math. Ann. 213 (1975) 153), and the double zeta function (First European Congress of Mathematics, Vol.
Masri, Riad
core +1 more source