A Proof of Moll’s Minimum Conjecture
نویسندگان
چکیده
Abstract. Let di(m) denote the coefficients of the Boros-Moll polynomials. Moll’s minimum conjecture states that the sequence {i(i+1)(d2i (m)−di−1(m)di+1(m))}1≤i≤m attains its minimum with i = m. This conjecture is a stronger than the log-concavity conjecture proved by Kausers and Paule. We give a proof of Moll’s conjecture by utilizing the spiral property of the sequence {di(m)}0≤i≤m, and the log-concavity of the sequence {i!di(m)}0≤i≤m.
منابع مشابه
Proof of Moll's minimum conjecture
Let di(m) denote the coefficients of the Boros-Moll polynomials. Moll’s minimum conjecture states that the sequence {i(i+1)(di (m)−di−1(m)di+1(m))}1≤i≤m attains its minimum at i = m with 2−2mm(m + 1) ( 2m m )2 . This conjecture is stronger than the log-concavity conjecture proved by Kauers and Paule. We give a proof of Moll’s conjecture by utilizing the spiral property of the sequence {di(m)}0≤...
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