## Uniform convergence of polynomials associated with varying Jacobi weights.(English)Zbl 0749.41011

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.

### MSC:

 41A10 Approximation by polynomials

### Keywords:

Jacobi weights; incomplete polynomials
Full Text:

### References:

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