The Greatest Lower Bound of a Boros–Moll Sequence

The Boros–Moll polynomials $P_m(a)$ arise in the evaluation of a quartic integral. In the past few years, there has been some remarkable research on the properties of the Boros–Moll coefficients. Chen and Gu gave a lower bound of the sequence $\{d^2_i(m)/d_{i-1}(m)d_{i+1}(m)\}$ for $m\geq2$, which is a stronger result than the log-concavity of the sequence $\{d_i(m)\}$. In this paper, we give the greatest lower bound for the sequence $\{d^2_i(m)/d_{i-1}(m)d_{i+1}(m)\}$.