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

Author:
Yoshihiro Takeyama

Journal:
Proc. Amer. Math. Soc. **137** (2009), 2997-3002

MSC (2000):
Primary 33D15, 05A30, 11M41

Published electronically:
May 4, 2009

MathSciNet review:
2506458

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the generating function for a -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 . 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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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:
https://doi.org/10.1090/S0002-9939-09-09931-6

Received by editor(s):
August 18, 2008

Published electronically:
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

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.