Sách Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences

Abstract
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 ≥ 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.