The Ratio Monotonicity of the Boros-Moll Polynomials

Details The Ratio Monotonicity of the Boros-Moll Polynomials The Ratio Monotonicity of the Boros-Moll Polynomials

2008-06-26

arxiv.org/abs/0806.4333v2

Mathematics

Combinatorics

14 pages, the final version, to appear in Mathematics of Computation

Scientific paper

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.

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