Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some rapidly converging series for $\zeta (2n+1)$


Author: H. M. Srivastava
Journal: Proc. Amer. Math. Soc. 127 (1999), 385-396
MSC (1991): Primary 11M06, 11M35, 33B15; Secondary 11B68, 33E20, 40A30
MathSciNet review: 1610797
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a natural number $n$, the author derives several families of series representations for the Riemann Zeta function $\zeta (2n+1)$. Each of these series representing $\zeta (2n+1)$ converges remarkably rapidly with its general term having the order estimate:

\begin{equation*}O(k^{-2n-1}\cdot m^{-2k})\qquad (k\to \infty ;\quad m=2,3,4,6).\end{equation*}

Relevant connections of the results presented here with many other known series representations for $\zeta (2n+1)$ are also pointed out.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11M06, 11M35, 33B15, 11B68, 33E20, 40A30

Retrieve articles in all journals with MSC (1991): 11M06, 11M35, 33B15, 11B68, 33E20, 40A30


Additional Information

H. M. Srivastava
Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4
Email: HMSRI@UVVM.UVIC.CA

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04945-X
PII: S 0002-9939(99)04945-X
Keywords: Zeta functions, binomial theorem, Pochhammer symbol, functional equation, harmonic numbers, l'H\^{o}pital's rule, Bernoulli numbers, Euler polynomials, Euler's formula
Received by editor(s): June 2, 1997
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society