6 problems

For $n=0,1,\dots$ and $\alpha>-1$, define the transitional Laguerre polynomials $\widehat{L}^{(\alpha)}_{n+1}(\cdot,t)$ by … where … Let the extreme zeros denote the smallest and l…

Let $\{p_n(x)\}_{n=m}^{\infty}$ be a family of exceptional orthogonal polynomials with weight function … where $W_0(x)$ is the weight function of a classical orthogonal polynomial…

Let $f$ be an entire function of positive, finite order $\lambda$, and let $p_n(z)$ denote its $n^\text{th}$ partial sum. Edrei–Saff–Varga's modified width conjecture. There exist…

Saff–Varga's width conjecture. There exists an infinite sequence of positive integers $N$ such that no region $S_\theta(\tau)$ is devoid of all zeros of all partial sums $p_n(z)$ w…

Let $H_{\lambda}(z)$ be the generalized Hermite polynomial associated with a partition $\lambda$. Veselov's conjecture. For any partition $\lambda$, the zeros of $H_{\lambda}(z)$ a…

Let the coefficients of the moments $m_{2l}$ be regarded as polynomials in the ensemble parameter $\kappa$, after extracting their stated powers of $N$ and $\kappa$. The coefficien…