2 problems

Let $\mu\geq 1$ and $k\geq\mu+1$ be nonnegative integers, let $f$ be associated with a real Legendre parameter $\lambda$, and fix $\lambda\neq 0,1$. Let $P_{\mu,k}$ be the correspo…

Let $f=x(x-1)(x-\lambda)$ be the Legendre cubic with three distinct real roots, so $\lambda\in\mathbb{R}\setminus\{0,1\}$. For each pair of indices $\mu,k$ considered in the paper,…