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Matematicheskie Zametki, 2022, Volume 111, Issue 1, paper published in the English version journal
(Mi mzm13119)
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Papers published in the English version of the journal
The Greatest Lower Bound of a Boros–Moll Sequence
Sabrina X. M. Panga, Lun Lvb, Jiaxue Wangb a School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, 050061 P. R. China
b School of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018 P. R. China
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
$\{d^2_i(m)/d_{i-1}(m)d_{i+1}(m)\}$.
Keywords:
Boros–Moll coefficients, log–concavity, greatest lower bound.
Received: 20.04.2021
Citation:
Sabrina X. M. Pang, Lun Lv, Jiaxue Wang, “The Greatest Lower Bound of a Boros–Moll Sequence”, Math. Notes, 111:1 (2022), 115–123
Linking options:
https://www.mathnet.ru/eng/mzm13119
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