Generalized log sine integrals and the Mordell-Tornheim zeta values
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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.References
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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
- Received by editor(s): December 6, 2008
- Received by editor(s) in revised form: June 1, 2009
- Published electronically: October 13, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 1463-1485
- MSC (2000): Primary 11M06, 11M35, 33E20
- DOI: https://doi.org/10.1090/S0002-9947-2010-05176-1
- MathSciNet review: 2737273