Results 11 to 20 of about 2,152 (201)
Hurwitz Zeta Function Is Prime [PDF]
Mathematics, 2023 We proved that the Hurwitz zeta function is prime. In addition, we derived the Nevanlinna characteristic for this function.
Marius Dundulis +3 more
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A New Family of Zeta Type Functions Involving the Hurwitz Zeta Function and the Alternating Hurwitz Zeta Function [PDF]
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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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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New Result of Analytic Functions Related to Hurwitz Zeta Function [PDF]
The Scientific World Journal, 2013 By using a linear operator, we obtain some new results for a normalized analytic function f defined by means of the Hadamard product of Hurwitz zeta function. A class related to this function will be introduced and the properties will be discussed.
F. Ghanim, M. Darus
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Derivatives of the Hurwitz Zeta function for rational arguments [PDF]
Journal of Computational and Applied Mathematics, 1998 The functional equation for the Hurwitz Zeta function ζ(s,a) is used to obtain formulas for derivatives of ζ(s,a) at negative odd s and rational a. For several of these rational arguments, closed-form expressions are given in terms of simpler transcendental functions, like the logarithm, the polygamma function, and the Riemann Zeta function.
Miller, Jeff, Adamchik, Victor S.
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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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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.
Robert Spira
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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.
Javtokas, A., Laurinčikas, A.
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Vanishing of the integral of the Hurwitz zeta Function [PDF]
Bulletin of the Australian Mathematical Society, 2002 A proof is given that the improper Riemann integral of ζ(s, a) with respect to the real parameter a, taken over the interval (0, 1], vanishes for all complex s with ℜ(s) < 1. The integral does not exist (as a finite real number) when ℜ(s) ≥ 1.
Kevin A. Broughan, Broughan, Kevin A.
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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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