5 problems

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…

Let $P_n(x)$ be the Boros–Moll polynomials, whose coefficients form a polynomial sequence in $n$. A polynomial sequence is infinitely $q$-log-convex if every iterate under the oper…

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…

Let $P_n(x)=\sum_{i=0}^n d_i(n)x^i$ be the Boros–Moll polynomial, so that $\{d_i(n)\}_{i=0}^n$ is its coefficient sequence. A finite nonnegative sequence is infinitely log-concave…

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…