Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 514, Issue 2, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2022.126330
Keywords
Riemann zeta function; Dirichlet beta function; Series representation; Acceleration formula; Asymptotically finite representation; Clausen function
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A parameterized family of series representations for the numbers zeta(2m + 1) is presented, where m is a positive integer. By utilizing Clausen functions of higher order, several conventional results are improved and generalized, leading to a significant improvement in the convergence rate. The parameterized family is also applicable to represent the numbers beta(2m) and derive asymptotically finite representations for both zeta(2m + 1) and beta(2m).
A parameterized family of series representations for the numbers zeta(2m + 1) is presented where m is a positive integer. Based on Clausen functions of higher order, several conventional results are improved and generalized; in particular, the rate of convergence can considerably be improved. The parameterized family is also applicable to represent the numbers beta(2m) and to derive asymptotically finite representations for both zeta(2m + 1) and beta(2m). (C) 2022 Elsevier Inc. All rights reserved.
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