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Fractional Calculus of the Lerch Zeta Function
Mediterranean Journal of Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Emanuel Guariglia, Guariglia Emanuel
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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 +3 more
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Subordination Properties of Meromorphic Kummer Function Correlated with Hurwitz–Lerch Zeta-Function
Mathematics, 2021 Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics.
Firas Ghanim +3 more
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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.
Robert Reynolds, Allan Stauffer
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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 +1 more
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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
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A note on a generalized double series. [PDF]
PLoS ONEBy employing contour integration the derivation of a generalized double finite series involving the Hurwitz-Lerch zeta function is used to derive closed form formulae in terms of special functions.
Robert Reynolds
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A note on the zeros of the Lerch zeta-function
Lietuvos Matematikos Rinkinys, 2001 In the paper we obtain the effective zero free regions for the Lerch zeta-function.
Ramūnas Garunkštis
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A Series Representation for the Hurwitz–Lerch Zeta Function [PDF]
Axioms, 2021 We derive a new formula for the Hurwitz–Lerch zeta function in terms of the infinite sum of the incomplete gamma function. Special cases are derived in terms of fundamental constants.
Robert Reynolds, Allan Stauffer
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The Lerch zeta function I. Zeta integrals [PDF]
Forum Mathematicum, 2012 Abstract. This is the first of four papers that study algebraic and analytic structures associated to the Lerch zeta function. This paper studies “zeta integrals” associated to the Lerch zeta function using test functions, and obtains functional equations for them.
Jeffrey C Lagarias, Wen-Ching Winnie Li
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