Abstract:
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
$\{d^2_i(m)/d_{i-1}(m)d_{i+1}(m)\}$.
