The lower envelope of ultraspherical polynomials

K. Castillo, S. Sadigova

Let $R_n^{(a,b)}=P_n^{(a,b)}/P_n^{(a,b)}(1)$ be the normalised Jacobi polynomials. For $\alpha \ge 0$, put ${\xi }_0=-1$ and let ${\xi }_n$ be the largest zero of $R_n^{(\alpha +1,\alpha )}$ for $n\ge 1$. We pr…