The Ratio Monotonicity of the Boros-Moll Polynomials
Combinatorics
2015-05-13 v2 Classical Analysis and ODEs
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 -log-concavity.
Cite
@article{arxiv.0806.4333,
title = {The Ratio Monotonicity of the Boros-Moll Polynomials},
author = {William Y. C. Chen and Ernest X. W. Xia},
journal= {arXiv preprint arXiv:0806.4333},
year = {2015}
}
Comments
14 pages, the final version, to appear in Mathematics of Computation