9 problems

Let $w_M$ be a weight supported on $(-1,1)$ such that $w_M(x)/(1+x)^{\beta}$ has a positive finite limit as $x\to -1$, and $w_M(x)/[-(1-x)^{\alpha}\log(1-x)]$ has a positive finite…

Let $m$ be an arbitrary nonzero integer, set $\eta=m\pi$, and consider the monic orthogonal polynomials associated with the weight $x\exp(im\pi x)$ on $[-1,1]$. Let $G_j(\eta^2)$ b…

Let $\eta$ be a positive zero of $J_0$, and consider the monic orthogonal polynomials associated with the weight $x(1-x^2)^{-1/2}\exp(i\eta x)$ on $[-1,1]$. Let $W_j(\eta^2)$ be mo…

Let $\zeta\in\mathbb{R}\setminus\{0\}$ be a zero of $J_{-1}$, and consider the monic orthogonal polynomials associated with the weight $(1-x^2)^{-1/2}\exp(i\zeta x)$ on $[-1,1]$. L…

Let $\lambda$, $\zeta$, $\alpha_n$, and $\beta_n$ be the parameters and recurrence coefficients associated with the monic orthogonal polynomials considered in the paper. For…

Generalized Krawtchouk uniqueness conjecture. There is only one initial value $y_0$ for which

Let $a_n$ and $b_n$ be the recurrence coefficients of the generalized Meixner polynomials, with parameters $a$, $\beta$, and $\gamma$, associated with the lattices $\mathbb{N}$ and…

Let $b_n$ be the recurrence coefficient of the generalized Charlier polynomials associated with the lattices $\mathbb{N}$, $\mathbb{N}+1-\beta$, and their bi-lattice. Charlier…

Let $a_n$ and $b_n$ be the recurrence coefficients of the generalized Charlier polynomials associated with the lattices $\mathbb{N}$, $\mathbb{N}+1-\beta$, and their bi-lattice, wi…