A Proof of Moll's Minimum Conjecture

Let \(d_i(m)\) denote the coefficients of the Boros-Moll polynomials. Moll's minimum conjecture states that the sequence \(\{i(i+1)(d_i^2(m)-d_{i-1}(m)d_{i+1}(m))\}_{1\leq i \leq m}\) attains its minimum with \(i=m\). This conjecture is a stronger than the log-concavity conjecture proved by Kau...

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Bibliographic Details
Published inarXiv.org
Main Authors Chen, William Y C, Xia, Ernest X W
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.04.2009
Subjects
Concavity
Polynomials
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Summary:Let \(d_i(m)\) denote the coefficients of the Boros-Moll polynomials. Moll's minimum conjecture states that the sequence \(\{i(i+1)(d_i^2(m)-d_{i-1}(m)d_{i+1}(m))\}_{1\leq i \leq m}\) attains its minimum with \(i=m\). This conjecture is a stronger than the log-concavity conjecture proved by Kausers and Paule. We give a proof of Moll's conjecture by utilizing the spiral property of the sequence \(\{d_i(m)\}_{0\leq i \leq m}\), and the log-concavity of the sequence \(\{i!d_i(m)\}_{0\leq i \leq m}\).
ISSN:2331-8422