2 problems

Let $\xi^N_0<\xi^N_1<\cdots<\xi^N_N$ be the LGL points, let $\Delta^N_k=[\xi^N_k,\xi^N_{k+1}]$, and define $q_k^N=|\Delta^N_k|/|\Delta^N_{k-1}|$ for the relevant indices. The famil…

Let $[a,b]$ be an interval, let $L=L_{[a,b]}:[a,(a+b)/2]\to[a,b]$ be given by $L(x)=2x-a$, and let $\{{\cal G}^{\mathrm{LGL}}_N\}_{N\in\mathbb{N}}$ be the family of Legendre–Gauss–…