6 problems

Let $P_m(a)=\sum_{i=0}^m d_i(m)a^i$ be the Boros-Moll polynomial. For $1\leq i\leq m$, define $u_i(m)=i(i+1)\bigl(d_i(m)^2-d_{i-1}(m)d_{i+1}(m)\bigr)$, with the coefficient sequenc…

For $m1$, define the BorosMoll polynomial $M_m(x)$ and its transform … A polynomial is symmetric if its coefficients read the same forwards and backwards, unimodal if its coefficie…

Brändén's conjecture for $R_n$. For any $n\geq 1$, the polynomial $R_n(x)$ has only real zeros. The paper presents this as the second real-rootedness conjecture related to the Boro…

Brändén's conjecture. The polynomial $R_m(x)$ has only real zeros for every positive integer $m$. The source states that the corresponding conjectures on derived polynomials imply…

Strong ratio monotonicity conjecture. The sequence

Infinite strict ratio-monotonicity conjecture. The Boros-Moll sequence $\{d_i(m)\}_{0\leq i\leq m}$ is $\infty$-strictly-ratio-monotone.