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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generalized log sine integrals and the Mordell-Tornheim zeta values


Author: Kazuhiro Onodera
Journal: Trans. Amer. Math. Soc. 363 (2011), 1463-1485
MSC (2000): Primary 11M06, 11M35, 33E20
Published electronically: October 13, 2010
MathSciNet review: 2737273
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Abstract: We introduce certain integrals of a product of the Bernoulli polynomials and logarithms of Milnor's multiple sine functions. It is shown that all the integrals are expressed by the Mordell-Tornheim zeta values at positive integers and that the converse is also true. Moreover, we apply the theory of the integral to obtain various new results for the Mordell-Tornheim zeta values.


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Additional Information

Kazuhiro Onodera
Affiliation: Department of Mathematics, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8551, Japan
Email: onodera@math.titech.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05176-1
PII: S 0002-9947(2010)05176-1
Keywords: Log sine integral, multiple zeta value, multiple sine function, Clausen function, Mordell-Tornheim zeta value
Received by editor(s): December 6, 2008
Received by editor(s) in revised form: June 1, 2009
Published electronically: October 13, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.