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Sum of multiple $ q$-zeta values

Author: Zhong-hua Li
Journal: Proc. Amer. Math. Soc. 138 (2010), 505-516
MSC (2000): Primary 11M41, 11M99
Published electronically: October 6, 2009
MathSciNet review: 2557168
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Abstract | References | Similar Articles | Additional Information

Abstract: The generating function of the sums of multiple $ q$-zeta values with fixed weights, depths and 1-heights, 2-heights, ..., $ r$-heights is represented in terms of specializations of basic hypergeometric functions.

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

  • 1. D. M. Bradley, Multiple $ q$-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 $ q$-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 $ i$-height, Math. Z., 258(2008), 133-142. MR 2350039 (2008j:11118)
  • 5. Y. Ohno and D. Zagier, Multiple zeta values of fixed weight, depth and height, Indag. Math. (N.S.), 12(2001), 483-487. MR 1908876 (2003e:11094)
  • 6. J. Okuda and Y. Takeyama, On relations for the multiple $ q$-zeta values, The Ramanujan Journal, 14(2007), 379-387. MR 2357443 (2008j:11011)
  • 7. M. Wachs and D. White, $ p,q$-Stirling numbers and set partition statistics, J. Combin. Theory Ser. A, 56(1991), 27-46. MR 1082841 (92b:05004)
  • 8. J. Zhao, multiple $ q$-zeta functions and multiple $ q$-polylogarithms, The Ramanujan Journal, 14 (2007), 189-221. MR 2341851 (2008h:11095)

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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

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
Published electronically: October 6, 2009
Communicated by: Ken Ono
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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