Results 31 to 40 of about 550,652 (221)
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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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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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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Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function [PDF]
, 2021 In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta functions.
Robert Reynolds, Allan Stauffer
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Journal of Mathematical Inequalities, 2019 . We study some equivalent conditions of a reverse Hilbert-type integral inequality with a particular non-homogeneous kernel and a best possible constant factor related to the extended Hurwitz-zeta function.
M. Rassias, 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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A weighted version of the Mishou theorem
Mathematical Modelling and Analysis, 2021 In 2007, H. Mishou obtained a joint universality theorem for the Riemann and Hurwitz zeta-functions ζ(s) and ζ(s,α) with transcendental parameter α on the approximation of a pair of analytic functions by shifts (ζ(s+iτ),ζ(s+iτ,α)), τ ∈R.
Antanas Laurinčikas +2 more
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The evaluation of Tornheim double sums. Part 1 [PDF]
, 2005 We provide an explicit formula for the Tornheim double series in terms of integrals involving the Hurwitz zeta function. We also study the limit when the parameters of the Tornheim sum become natural numbers, and show that in that case it can be ...
Espinosa, Olivier, Moll, Victor H.
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Note on the Hurwitz zeta-function [PDF]
Proceedings of the American Mathematical Society, 1951 Received by the editors June 10, 1950. 1 This work is an offshoot of investigations carried out under the auspices of the Office of Naval Research, Contract N9-ONR90,000. 2 B. Riemann, Ueber die Anzahl der Primzahlen unter einer gegebenen Grbsse, Monatsberichte der Preussischeni Akademie der Wissenschaften (1859, 1860) pp. 671680. 3A.
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