2-Log-concavity of the Boros-Moll Polynomials
Chen, William Y. C. · Xia, Ernest X. W.
الأصل · EN
The Boros-Moll polynomials Pₘ(a) arise in the evaluation of a quartic integral. It has been conjectured by Boros and Moll that these polynomials are infinitely log-concave. In this paper, we show that Pₘ(a) is 2-log-concave for any m≥ 2. Let dᵢ(m) be the coefficient of aⁱ in Pₘ(a). We also show that the sequence {i (i+1)(dᵢ²(m)-dᵢ₋₁(m)dᵢ₊₁(m))}₁≤ ᵢ ≤ ₘ is log-concave. This leads another proof of Moll's minimum conjecture.
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