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≤i≤m, and the log-concavity of the sequence {i!di(m)}0≤i≤m.