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A $ q$-analogue of non-strict multiple zeta values and basic hypergeometric series

Author(s): Yoshihiro Takeyama
Journal: Proc. Amer. Math. Soc. 137 (2009), 2997-3002.
MSC (2000): Primary 33D15, 05A30, 11M41
Posted: May 4, 2009
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Abstract: We consider the generating function for a $ q$-analogue of non-strict multiple zeta values (or multiple zeta-star values) and prove an explicit formula for it in terms of a basic hypergeometric series $ {}_{3}\phi_{2}$. By specializing the variables in the generating function, we reproduce the sum formula obtained by Ohno and Okuda and get some relations in the case of full height.

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Takashi Aoki, Yasuo Ohno and Noriko Wakabayashi, Multiple zeta-star values with fixed weight, depth and $ i$-heights and generalized hypergeometric functions, in preparation.

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Additional Information:

Yoshihiro Takeyama
Affiliation: Department of Mathematics, Graduate School of Pure and Applied Sciences, Tsukuba University, Tsukuba, Ibaraki 305-8571, Japan
Email: takeyama@math.tsukuba.ac.jp

DOI: 10.1090/S0002-9939-09-09931-6
PII: S 0002-9939(09)09931-6
Received by editor(s): August 18, 2008
Posted: May 4, 2009
Additional Notes: The research of the author was supported by Grant-in-Aid for Young Scientists (B) No. 20740088
Communicated by: Peter A. Clarkson
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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