Results 41 to 50 of about 36,426 (206)

Is Catalan’s Constant Rational?

Mathematics, 2022
This paper employs a contour integral method to derive and evaluate the infinite sum of the Euler polynomial expressed in terms of the Hurwitz Zeta function. We provide formulae for several classes of infinite sums of the Euler polynomial in terms of the
Robert Reynolds, Allan Stauffer
doaj   +1 more source

An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions

, 2007
This paper sketches a technique for improving the rate of convergence of a general oscillatory sequence, and then applies this series acceleration algorithm to the polylogarithm and the Hurwitz zeta function.
A. Jonquière, C. Brezinski, E.A. Karatsuba, E.J. Weniger, E.P. Balanzario, G. Soff, H. Cohen, H. Hasse, Linas Vepštas, R. Šleževičiene, T.M. Apostol   +10 more
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The Mean Square of the Hurwitz Zeta-Function in Short Intervals

Axioms
The Hurwitz zeta-function ζ(s,α), s=σ+it, with parameter ...
A. Laurinčikas, D. Šiaučiūnas
semanticscholar   +1 more source

Asymptotics to all orders of the Hurwitz zeta function [PDF]

Journal of Mathematical Analysis and Applications, 2017
We present several formulae for the large-t asymptotics of the modified Hurwitz zeta function ζ 1 ( x , s ) , x > 0 , s = σ + i t , 0 σ ≤ 1 , t > 0 , which are valid to all orders.
A. Fernandez, A. Fokas
semanticscholar   +1 more source

Series Representations at Special Values of Generalized Hurwitz-Lerch Zeta Function

Abstract and Applied Analysis, 2013
By making use of some explicit relationships between the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Frobenius-Euler polynomials of higher order and the generalized Hurwitz-Lerch zeta function as well as a new expansion formula for ...
S. Gaboury, A. Bayad
doaj   +1 more source

Joint universality of some zeta-functions. I

Lietuvos Matematikos Rinkinys, 2010
In the paper, the joint universality for the Riemann zeta-function and a collection of periodic Hurwitz zeta functions is discussed and basic results are given.
Santa Račkauskienė, Darius Šiaučiūnas   +1 more
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Remarks on the mixed joint universality for a class of zeta-functions

, 2016
Two remarks related with the mixed joint universality for a polynomial Euler product and a periodic Hurwitz zeta-function with a transcendental parameter are given.
Hilbert, Javtokas, Kačinskaitė, KOHJI MATSUMOTO, Laurinčikas, Laurinčikas, Laurinčikas, Matsumoto, ROMA KAČINSKAITĖ, Steuding, Voronin   +10 more
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Analytic Continuation of the Hurwitz Transform

Mathematics
An integral over the unit interval of the product of a given function and the Hurwitz zeta function is known as the Hurwitz transform of the function. We give sufficient conditions on the function for the Hurwitz transform to continue meromorphically to ...
Namhoon Kim
doaj   +1 more source

Questions around the nontrivial zeros of the Riemann zeta-function. Computations and classifications

Mathematical Modelling and Analysis, 2011
We study the sequence of nontrivial zeros of the Riemann zeta-function with respect to sequences of zeros of other related functions, namely, the Hurwitz zeta-function and the derivative of Riemann's zeta-function.
Ramūnas Garunkštis, Joern Steuding
doaj   +1 more source

Integral representations of q-analogues of the Hurwitz zeta function

, 2005
Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of ...
DM Bradley, ET Whittaker, GE Andrews, H Tsumura, H Tsumura, J Satoh, M Kaneko, Masato Wakayama, N Koblitz, N Kurokawa, P Appell, Y Hashimoto, Yoshinori Yamasaki   +12 more
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