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≥2 , 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)} .