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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the sum formula for the $ q$-analogue of non-strict multiple zeta values


Authors: Yasuo Ohno and Jun-Ichi Okuda
Journal: Proc. Amer. Math. Soc. 135 (2007), 3029-3037
MSC (2000): Primary 11M41, 33D15, 11B65, 05A30, 11M06
Published electronically: June 19, 2007
MathSciNet review: 2322731
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Abstract: In this article, the $ q$-analogues of the linear relations of non-strict multiple zeta values called ``the sum formula'' and ``the cyclic sum formula'' are established.


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Additional Information

Yasuo Ohno
Affiliation: Department of Mathematics, Kinki University, Higashi-Osaka 577-8502, Japan
Address at time of publication: Max-Planck-Institute für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
Email: ohno@math.kindai.ac.jp

Jun-Ichi Okuda
Affiliation: Department of Mathematical Sciences, Science and Engineering, Waseda University, Tokyo 169-8555, Japan
Email: okuda@gm.math.waseda.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08994-0
PII: S 0002-9939(07)08994-0
Keywords: Multiple zeta values, non-strict multiple zeta values, multiple zeta star values, sum formula, $q$-analogue, $q$-series, basic hypergeometric function.
Received by editor(s): March 1, 2006
Published electronically: June 19, 2007
Additional Notes: The first author was partly supported by Grant-in-Aid for Young Scientists (B) No. 18740020 and the second author was partly supported by Grant-in-Aid for Young Scientists (B) No. 17740026 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.