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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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On the periodic Hurwitz zeta-function. [PDF]
Hardy-Ramanujan Journal, 2006 In this paper, an universality theorem in the Voronin sense for the periodic Hurwitz zeta-function is proved.
A. Javtokas, Antanas Laurinčikas
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On the Hurwitz zeta function with an application to the beta-exponential distribution
Journal of Inequalities and Applications, 2020 We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders.
Julyan Arbel +2 more
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Analytical properties of the Hurwitz–Lerch zeta function
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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On the product of Hurwitz zeta-functions [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2017 Corresponding to the lattice point problem for a random sphere Kendall and Rankin [8], Nakajima [9] considered the summatory function of the coefficients of the product of two Hurwitz zeta-functions and obtained the Bessel series expression. In this note we treat the case of the product of $\varkappa$ Hurwitz zeta-functions for an arbitrary integer ...
Wang, Nian Liang, Banerjee, Soumyarup
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A Series Representation for the Hurwitz–Lerch Zeta Function
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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Joint discrete approximation of a pair of analytic functions by periodic zeta-functions
Mathematical Modelling and Analysis, 2020 In the paper, the problem of simultaneous approximation of a pair of analytic functions by a pair of discrete shifts of the periodic and periodic Hurwitz zeta-function is considered. The above shifts are defined by using the sequence of imaginary parts of
Aidas Balčiūnas +5 more
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Zeros of Hurwitz zeta functions [PDF]
Mathematics of Computation, 1976 All complex zeros of each Hurwitz zeta function are shown to lie in a vertical strip. Trivial real zeros analogous to those for the Riemann zeta function are found. Zeros of two particular Hurwitz zeta functions are calculated.
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Journal of Mathematical Inequalities, 2020 . By using the way of real analysis and the weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related the extended Hurwitz zeta function
Aizhen Wang, Bicheng Yang
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On Hardy-type integral inequalities in the whole plane related to the extended Hurwitz-zeta function
, 2020 Using weight functions, we establish a few equivalent statements of two kinds of Hardy-type integral inequalities with nonhomogeneous kernel in the whole plane.
M. Rassias +2 more
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