Results 1 to 10 of about 2,163 (157)

Extended Wang sum and associated products. [PDF]

PLoS One, 2022
The Wang sum involving the exponential sums of Lerch's Zeta functions is extended to the finite sum of the Huwitz-Lerch Zeta function to derive sums and products involving cosine and tangent trigonometric functions.
Reynolds R, Stauffer A.
europepmc   +2 more sources

The Lerch Zeta Function II. Analytic Continuation [PDF]

Forum Mathematicum, 2010
This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. In this paper we analytically continue it as a function of three complex variables.
Apostol T. M., Barnes E. W., Berndt B., Hurwitz A., Lipschitz M., Lipschitz M., Mikolas M., Oberhettinger E.   +7 more
core   +3 more sources

Analytical properties of the Hurwitz–Lerch zeta function [PDF]

Advances in Difference Equations, 2020
In the present paper, we aim to extend the Hurwitz–Lerch zeta function Φ δ , ς ; γ ( ξ , s , υ ; p ) $\varPhi _{\delta ,\varsigma ;\gamma }(\xi ,s,\upsilon ;p)$ involving the extension of the beta function (Choi et al. in Honam Math. J.
Raghib Nadeem, Talha Usman, Kottakkaran Sooppy Nisar, Dumitru Baleanu   +3 more
doaj   +3 more sources

On the Order of Growth of Lerch Zeta Functions

Mathematics, 2023
We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t13/84+ϵ as t → ∞.
Jörn Steuding, Janyarak Tongsomporn
doaj   +3 more sources

Analytic study and statistical enforcement of extended beta functions imposed by Mittag-Leffler and Hurwitz-Lerch Zeta functions. [PDF]

MethodsX
Special Function Theory is used in many mathematical fields to model scientific progress, from theoretical to practical. This helps efficiently analyze the newly expanded Beta class of functions on a complicated domain.
Abdulnabi FF, Al-Janaby HF, Ghanim F.
europepmc   +2 more sources

Further Extension of the Generalized Hurwitz-Lerch Zeta Function of Two Variables

Mathematics, 2019
The main aim of this paper is to provide a new generalization of Hurwitz-Lerch Zeta function of two variables. We also investigate several interesting properties such as integral representations, summation formula, and a connection with the generalized ...
Kottakkaran Sooppy Nisar
doaj   +3 more sources

A joint limit theorem for Lerch zeta-function

Lietuvos Matematikos Rinkinys, 1998
There is not abstract.
Antanas Laurinčikas
doaj   +4 more sources

Joint universality of the Riemann zeta-function and Lerch zeta-functions

Nonlinear Analysis, 2013
In the paper, we prove a joint universality theorem for the Riemann zeta-function and a collection of Lerch zeta-functions with parameters algebraically independent over the field of rational numbers.
Antanas Laurinčikas, Renata Macaitienė˙   +1 more
doaj   +4 more sources

Extended Levett trigonometric series. [PDF]

PLoS One
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 R.
europepmc   +2 more sources

Extended Prudnikov sum

AIMS Mathematics, 2022
A Prudnikov sum is extended to derive the finite sum of the Hurwitz-Lerch Zeta function in terms of the Hurwitz-Lerch Zeta function. This formula is then used to evaluate a number trigonometric sums and products in terms of other trigonometric functions.
Robert Reynolds, Allan Stauffer
doaj   +1 more source