Uniform convergence of polynomials associated with varying Jacobi weights (Q1178588)

This article determines the functions on \([-1,1]\) that are uniform limits of weighted polynomials of the form \((1-x)^{\alpha_ n}(1+x)^{\beta_ n}p_ n(x)\), where \(\deg p_ n\leq n\), \(\lim_{n\to\infty}\alpha_ n/n=\theta_ 1\geq 0\) and \(\lim_{n\to\infty}\beta_ n/n=\theta_ 2\geq 0\). Estimates for the rate of convergence are also obtained. These results confirm a conjecture of Saff and extend previous results for incomplete polynomials.