The ratio monotonicity of the Boros-Moll polynomials

Chen, William; Xia, Ernest

doi:10.1090/S0025-5718-09-02223-6

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.

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