The ratio monotonicity of the Boros-Moll polynomials
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- by William Y. C. Chen and Ernest X. W. Xia PDF
- Math. Comp. 78 (2009), 2269-2282 Request permission
Abstract:
In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that these polynomials are log-concave. In this paper, we show that the Boros-Moll polynomials possess the ratio monotone property which implies the log-concavity and the spiral property. We conclude with a conjecture which is stronger than Moll’s conjecture on the $\infty$-log-concavity.References
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Additional 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
- Ernest X. W. Xia
- Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
- Email: xxw@cfc.nankai.edu.cn
- Received by editor(s): June 26, 2008
- Received by editor(s) in revised form: September 26, 2008
- Published electronically: February 11, 2009
- Additional Notes: This work was supported by the 973 Project, the PCSIRT Project of the Ministry of Education, the Ministry of Science and Technology, and the National Science Foundation of China.
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 78 (2009), 2269-2282
- MSC (2000): Primary 05A20, 33F10
- DOI: https://doi.org/10.1090/S0025-5718-09-02223-6
- MathSciNet review: 2521289