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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
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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
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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
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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
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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
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One functional property of the Lerch zeta-function

Lietuvos Matematikos Rinkinys, 1998
There is not abstract.
Antanas Laurinčikas
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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
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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