The Reverse Ultra Log-Concavity of the Boros-Moll Polynomials

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dc.creatorChen, William Y. C.
dc.creatorGu, Cindy C. Y.
dc.date2008-08-31
dc.date2009-04-24
dc.date.accessioned2026-07-07T13:07:33Z
dc.date.available2026-07-07T13:07:33Z
dc.descriptionWe 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 $m\geq 2$.
dc.description9 pages; Final version, to appear in Proc. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/0809.0127
dc.identifierhttp://arxiv.org/abs/0809.0127
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228123
dc.subjectCombinatorics
dc.subjectClassical Analysis and ODEs
dc.titleThe Reverse Ultra Log-Concavity of the Boros-Moll Polynomials
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