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Some approximations with Hurwitz zeta function
Filomat, 2020 In this paper, we focus on some approximations with Hurwitz zeta function. By using these approximations, we present some asymptotic formulae related to Hurwitz zeta function. As an application, we give two corollaries related to Bernoulli polynomials.
Aykut Ahmet Aygunes
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Power mean of the Hurwitz zeta function
, 2018 In this note we derive asymptotic formulas for power mean of the Hurwitz zeta function over large intervals.
A. C. L. Ashton
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Asymptotic expansions for the alternating Hurwitz zeta function and its derivatives [PDF]
Journal of Mathematical Analysis and Applications, 2021 Su Hu, Min-Soo Kim
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Remark on the Hurwitz zeta function [PDF]
Proceedings of the American Mathematical Society, 1951 T. M. Apostol
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Linear operators, the Hurwitz zeta function and Dirichlet L-functions [PDF]
Journal of Number Theory, 2019 Bernardo Bianco Prado, Kim Klinger-Logan
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AIMS Mathematics, 2022 A Prudnikov sum is extended to derive the finite sum of the Hurwitz-Lerch Zeta function in terms of the Hurwitz-Lerch Zeta function. This formula is then used to evaluate a number trigonometric sums and products in terms of other trigonometric functions.
Robert Reynolds, Allan Stauffer
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On the Mishou Theorem for Zeta-Functions with Periodic Coefficients
Mathematics, 2023 Let a={am} and b={bm} be two periodic sequences of complex numbers, and, additionally, a is multiplicative. In this paper, the joint approximation of a pair of analytic functions by shifts (ζnT(s+iτ;a),ζnT(s+iτ,α;b)) of absolutely convergent Dirichlet ...
Aidas Balčiūnas +3 more
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Mathematical Modelling and Analysis, 2023 In the paper, we construct an absolutely convergent Dirichlet series which in the mean is close to the periodic Hurwitz zeta-function, and has the universality property on the approximation of a wide class of analytic functions.
A. Balčiūnas +2 more
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Moments of the Hurwitz zeta function on the critical line
Mathematical Proceedings of the Cambridge Philosophical Society, 2022 We study the moments $M_k(T;\,\alpha) = \int_T^{2T} |\zeta(s,\alpha)|^{2k}\,dt$ of the Hurwitz zeta function $\zeta(s,\alpha)$ on the critical line, $s = 1/2 + it$ with a rational shift $\alpha \in \mathbb{Q}$ . We conjecture, in analogy with the
A. Sahay
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Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function
Mathematics, 2021 We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it to derive the infinite sum of the Incomplete gamma function in terms of the Hurwitz zeta function.
Robert Reynolds, Allan Stauffer
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