2 problems

Jacobi zero-preservation conjecture. If $\alpha$ and $\beta$ are non-negative integers, then $T_{\alpha,\beta}$ preserves the set of polynomials whose zeros lie only in $(-1,1)$. T…

Let $f(x)=\sum_{k=0}^n a_kx^k\in\mathbb{R}[x]$ have all its zeros in $(-1,1)$, and define the linear transformation $T$ by … where $P_k(x)$ is the $k$-th Legendre polynomial. Fisk'…