7 problems

Let $c>1$ and $0<\varepsilon<1$ be real numbers, and let $n>0$ be an integer. Let $\lambda_n$ denote the prolate spheroidal eigenvalue. Eigenvalue-decay conjecture. If … then … Thi…

Let $c>0$, let $n>2c/\pi$ be an integer, and let $m$ be an integer with $0\leq m<n$. Let $\delta_n(\psi_m)$ be the quadrature error for the prolate spheroidal wave function…

Let $c>1$ be real, let $n>2c/\pi$ be an integer, and let $S_n$ be the stated quadrature rule. For even integers $m$ with $0\leq m<n$, let $\delta_n(\psi_m)$ be the quadrature error…

Let $c>0$ and $a\geq 0$ be real numbers, and let $n>2c/\pi$ be an integer. Let $\delta_n(e^{icax})$ denote the quadrature error associated with the quadrature nodes $t_j$ and weigh…

Exponential quadrature-error conjecture. The quadrature error for the exponential function satisfies

Quadrature-error conjecture. The quadrature error satisfies

Relative-accuracy conjecture. The coordinates of $\beta^{(n)}$ satisfy, for every $1\leq k\leq N$,