Qi-Feng Bai

The Erd\'elyi--Magnus--Nevai and Krasikov Conjectures for Jacobi Polynomials

Let $p_n^{(\alpha,\beta)}$ denote the Jacobi polynomial orthonormal for the weight $(1-x)^\alpha(1+x)^\beta$ on $[-1,1]$, where $\alpha,\beta\ge-1/2$, and put $S=\alpha+\beta+1$. We prove the uniform degree--parameter estimate $$ (1-x)^{\alpha+1/2}(1+x)^{\beta+1/2} \bigl|p_n^{(\alpha,\beta)}(x)\bigr|^2 \le C\max\bigl\{...