5 problems

Let $d_\ell(m)$ be the coefficient of $x^\ell$ in the Boros-Moll polynomial $P_m(x)$. For a sequence $\{a_i\}_{i\geq 0}$, let…

Let $d_\ell(m)$ be the coefficient of $x^\ell$ in the Boros-Moll polynomial $P_m(x)$. For fixed $m$, consider the ratio sequence $d_\ell(m)/d_{\ell-1}(m)$. Ratio-shape conjecture.…

Let $d_\ell(m)$ be the coefficient of $x^\ell$ in the Boros-Moll polynomial $P_m(x)$. For each fixed $\ell\geq 0$, define the sequence $a_m=d_\ell(m-1)d_\ell(m+1)/d_\ell^2(m)$ for…

Let $d_\ell(m)$ be the coefficient of $x^\ell$ in the Boros-Moll polynomial $P_m(x)$, and consider, for fixed $\ell$, the transposed sequence $\{d_\ell(m)\}_{m\geq\ell}$. Let…

Let $d_\ell(m)$ denote the coefficient of $x^\ell$ in the Boros-Moll polynomial $P_m(x)$, for $0\leq \ell\leq m$. A sequence is $k$-log-concave when its first $k$ iterates under th…