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2-Log-Concavity of the Boros–Moll Polynomials

Published online by Cambridge University Press:  21 August 2013

William Y. C. Chen  and
Ernest X. W. Xia
William Y. C. Chen
Affiliation:
Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People's Republic of China (chen@nankai.edu.cn)
Ernest X. W. Xia
Affiliation:
Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013, People's Republic of China (ernestxwxia@163.com)
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Abstract

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The Boros–Moll polynomials Pm (a) arise in the evaluation of a quartic integral. It has been conjectured by Boros and Moll that these polynomials are infinitely log-concave. In this paper, we show that Pm (a) is 2-log-concave for any m ≥ 2. Let di (m) be the coefficient of ai in Pm (a). We also show that the sequence is log-concave.

Keywords

2-log-concavityBoros–Moll polynomialquartic integralPrimary 05A1005A20Secondary 33F10
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 3 , October 2013 , pp. 701 - 722
Copyright
Copyright © Edinburgh Mathematical Society 2013 

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