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Sum of multiple  -zeta values
Author(s):
Zhong-hua
Li
Journal:
Proc. Amer. Math. Soc.
138
(2010),
505-516.
MSC (2000):
Primary 11M41, 11M99
Posted:
October 6, 2009
MathSciNet review:
2557168
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Additional information
Abstract:
The generating function of the sums of multiple  -zeta values with fixed weights, depths and 1-heights, 2-heights, ...,  -heights is represented in terms of specializations of basic hypergeometric functions.
References:
-
- 1.
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 -zeta values, J. Algebra, 283(2005), 752-798. MR 2111222 (2006f:11106) - 2.
- G. Gasper and M. Rahman, Basic hypergeometric series, second edition, Cambridge University Press, Cambridge (England) and New York, 2004. MR 2128719 (2006d:33028)
- 3.
- H. W. Gould, The
 -Stirling numbers of the first and second kinds, Duke Math. J., 28(1961), 281-289. MR 0122759 (23:A99) - 4.
- Z. Li, Sum of multiple zeta values of fixed weight, depth and
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- 6.
- J. Okuda and Y. Takeyama, On relations for the multiple
 -zeta values, The Ramanujan Journal, 14(2007), 379-387. MR 2357443 (2008j:11011) - 7.
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- J. Zhao, multiple
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Additional Information:
Zhong-hua
Li
Affiliation:
Graduate School of Mathematical Science, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan
Address at time of publication:
Department of Mathematics, Tongji University, Shanghai 200092, People's Republic of China
Email:
lizhmath@gmail.com
DOI:
10.1090/S0002-9939-09-10096-5
PII:
S 0002-9939(09)10096-5
Keywords:
Multiple $q$-zeta values,
multiple $q$-polylogarithms,
basic hypergeometric functions
Received by editor(s):
March 1, 2009,
Received by editor(s) in revised form:
June 20, 2009
Posted:
October 6, 2009
Communicated by:
Ken Ono
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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