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SYMMETRIC FUNCTIONS AND MULTIPLE ZETA VALUES

Part of: Zeta and $L$-functions: analytic theory Acceleration of convergence Elementary classical functions

Published online by Cambridge University Press:  24 July 2019

WENCHANG CHU Open the ORCID record for WENCHANG CHU [Opens in a new window]
WENCHANG CHU*
Affiliation:
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou (Henan), P. R. China email chu.wenchang@unisalento.it
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Abstract

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Four classes of multiple series, which can be considered as multifold counterparts of four classical summation formulae related to the Riemann zeta series, are evaluated in closed form.

Keywords

Riemann zeta functionelementary symmetric functioncomplete symmetric functionBernoulli numberEuler number

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$
Secondary: 33B10: Exponential and trigonometric functions 65B10: Summation of series
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 3 , June 2020 , pp. 426 - 437
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

Footnotes

†

Current address: Department of Mathematics and Physics, University of Salento, PO Box 193, 73100 Lecce, Italy

References

Borwein, J. M., Bradley, D. M. and Broadhurst, D. J., ‘Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k’, Electron. J. Combin. 4(2) (1997), Article ID R5.Google Scholar
Chu, W., ‘Symmetric functions and the Riemann zeta series’, Indian J. Pure Appl. Math. 31(12) (2000), 1677–1689.Google Scholar
Comtet, L., Advanced Combinatorics (Dordrecht–Holland, The Netherlands, 1974).Google Scholar
Graham, R. L., Knuth, D. E. and Patashnik, O., Concrete Mathematics (Addison-Wesley Publishing Company, Reading, MA, 1989).Google Scholar
Hoffman, M. E., ‘Multiple harmonic series’, Pacific J. Math. 152 (1992), 275–290.Google Scholar
Macdonald, I. G., Symmetric Functions and Hall Polynomials (Oxford University Press, London–New York, 1979).Google Scholar
Merca, M., ‘Asymptotics of the Chebyshev–Stirling numbers of the first kind’, Integral Transforms Spec. Funct. 27(4) (2016), 259–267.10.1080/10652469.2015.1117460Google Scholar
Nakamura, T., ‘Bernoulli numbers and multiple zeta values’, Proc. Japan Acad. Ser. A 81(2) (2005), 21–22.10.3792/pjaa.81.21Google Scholar
Sloane, N. J. A., The Online Encyclopedia of Integer Sequences, https://oeis.org/.Google Scholar
Stromberg, K. R., An Introduction to Classical Real Analysis (Wadsworth, Belmont, CA, 1981).Google Scholar
Zagier, D., ‘Evaluation of the multiple zeta values 𝜁(2, …, 2, 3, 2, …, 2)’, Ann. of Math. (2) 175 (2012), 977–1000.10.4007/annals.2012.175.2.11Google Scholar