Results 11 to 20 of about 107 (92)
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 0003, Allan Stauffer
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Applications ~of $Q$-hypergeometric and Hurwitz-Lerch Zeta Functions on Meromorphic Functions [PDF]
Mathematics Interdisciplinary Research, 2023 A new subclass of meromorphic univalent functions by using the q-hypergeometric and Hurwitz-Lerch Zeta functions is defined. Also, by applying the generalized Liu-Srivastava operator on meromorphic functions, some geometric properties of the new ...
Seyed Hadi Sayedain Boroujeni +1 more
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Analytical properties of the Hurwitz–Lerch zeta function [PDF]
Advances in Difference Equations, 2020 AbstractIn the present paper, we aim to extend the Hurwitz–Lerch zeta function $\varPhi _{\delta ,\varsigma ;\gamma }(\xi ,s,\upsilon ;p)$ Φ δ , ς ; γ ( ξ , s , υ ; p ) involving the extension of the beta function (Choi et al. in Honam Math. J. 36(2):357–385, 2014).
Raghib Nadeem +3 more
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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
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Mathematics, 2021 In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions,
Daeyeoul Kim, Yilmaz Simsek
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Ural Mathematical Journal, 2022 With a possible connection to integrals used in General Relativity, we used our contour integral method to write a closed form solution for a quadruple integral involving exponential functions and logarithm of quotient radicals.
Robert Reynolds, Allan Stauffer
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Some Weighted Sum Formulas for Multiple Zeta, Hurwitz Zeta, and Alternating Multiple Zeta Values
Journal of Mathematics, 2021 We perform a further investigation for the multiple zeta values and their variations and generalizations in this paper. By making use of the method of the generating functions and some connections between the higher-order trigonometric functions and the ...
Yuan He, Zhuoyu Chen
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A family of incomplete Hurwitz-Lerch zeta functions of two variables [PDF]
Miskolc Mathematical Notes, 2020 Inspired essentially by the work [H. M. Srivastava, M. A. Chaudhry and R. P. Agarwal [The incomplete Pochhammer symbols and their applications to hypergeometric and related functions, Integral Transforms Spec. Funct. 23 (2012), 659-683] (see [16])], we introduce the families of the incomplete Hurwitz-Lerch Zeta functions of two variables.
Srivastava, H. M. +2 more
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On extended Hurwitz–Lerch zeta function
Journal of Mathematical Analysis and Applications, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luo, Min-Jie +2 more
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Real zeros of Hurwitz–Lerch zeta and Hurwitz–Lerch type of Euler–Zagier double zeta functions [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2015 AbstractLet 0 < a ⩽ 1, s, z ∈ ${\mathbb{C}}$ and 0 < |z| ⩽ 1. Then the Hurwitz–Lerch zeta function is defined by Φ(s, a, z) ≔ ∑∞n = 0zn(n + a)− s when σ ≔ ℜ(s) > 1. In this paper, we show that the Hurwitz zeta function ζ(σ, a) ≔ Φ(σ, a, 1) does not vanish for all 0 < σ < 1 if and only if a ⩾ 1/2.
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