The ratio monotonicity of the Boros-Moll polynomials
نویسندگان
چکیده
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 logconcave. 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.
منابع مشابه
Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences
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 Mart́ınez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Che...
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ورودعنوان ژورنال:
- Math. Comput.
دوره 78 شماره
صفحات -
تاریخ انتشار 2009