arXiv 1007.50172010-07-28math.COmath.CA

Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences

William Y. C. Chen, Arthur L. B. Yang, Elaine L. F. Zhou

备注：: 9 pages

英文摘要：

The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P(x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P(x+1), which leads to the log-concavity of P(x+c) for any $c\geq 1$ due to Llamas and Mart\'ınez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Chen and Xia without resorting to the recurrence relations of the coefficients.

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