Results 1 to 10 of about 2,855 (137)

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

Mock theta functions and Appell–Lerch sums [PDF]

Journal of Inequalities and Applications, 2018
Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function g2(x,q) $g_{2}{(x,q)}$.
Bin Chen
doaj   +3 more sources

Zeros of the lerch transcendent function

Mathematical Modelling and Analysis, 2012
We investigate the distribution of zeros of the Lerch transcendent function We find an upper and lower estimates of zeros of the function Φ(q,s,a) in any rectangle {s : σ1 < Re s < σ2 ≤ 1.73…, 0 < Im s ≤ T}.
Ramūnas Garunkštis, Andrius Grigutis
doaj   +5 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.
Faten F. Abdulnabi, Hiba F. Al-Janaby, Firas Ghanim   +2 more
doaj   +2 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.
Robert Reynolds
doaj   +2 more sources

One functional property of the Lerch zeta-function

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

On Discrete Approximation of Analytic Functions by Shifts of the Lerch Zeta Function

Mathematics, 2022
The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters and a
Audronė Rimkevičienė, Darius Šiaučiūnas   +1 more
doaj   +1 more source

Extended Wang sum and associated products.

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.
Robert Reynolds, Allan Stauffer
doaj   +1 more source

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   +1 more source

Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation

Journal of Mathematics, 2022
We consider a Hurwitz-Lerch zeta function Φs,z,a sum over the natural numbers. We provide an analytically continued closed form solution for this sum in terms of the addition of Hurwitz-Lerch zeta functions.
Robert Reynolds, Allan Stauffer
doaj   +1 more source