The reverse ultra log-concavity of the Boros-Moll polynomials
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- by William Y. C. Chen and Cindy C. Y. Gu
- Proc. Amer. Math. Soc. 137 (2009), 3991-3998
- DOI: https://doi.org/10.1090/S0002-9939-09-09976-6
- Published electronically: July 21, 2009
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Abstract:
We prove the reverse ultra log-concavity of the Boros-Moll polynomials. We further establish an inequality which implies the log-concavity of the sequence $\{i!d_i(m)\}$ for any $m\geq 2$, where $d_i(m)$ are the coefficients of the Boros-Moll polynomials $P_m(a)$. This inequality also leads to the fact that in the asymptotic sense, the Boros-Moll sequences are just on the borderline between ultra log-concavity and reverse ultra log-concavity. We propose two conjectures on the log-concavity and reverse ultra log-concavity of the sequence $\{d_{i-1}(m) d_{i+1}(m)/d_i(m)^2\}$ for $m\geq 2$.References
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Bibliographic Information
- William Y. C. Chen
- Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
- MR Author ID: 232802
- Email: chen@nankai.edu.cn
- Cindy C. Y. Gu
- Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
- Email: guchunyan@cfc.nankai.edu.cn
- Received by editor(s): August 31, 2008
- Received by editor(s) in revised form: March 23, 2009
- Published electronically: July 21, 2009
- Communicated by: Jim Haglund
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3991-3998
- MSC (2000): Primary 05A20, 33F10
- DOI: https://doi.org/10.1090/S0002-9939-09-09976-6
- MathSciNet review: 2538559