The Valleé-Poussin Means for Special Series With Respect to Ultraspherical Jacobi Polynomials With Sticking Partial Sums

Abstract

The authors continue study of special series with sticking property (r-fold coincidence at points ± 1) in ultraspherical Jacobi polynomials, that was started in the previous works of the first author. In the present paper they are dealing with an approximative properties of Vallee-Poussin means for partial sums of the mentioned special series. It is shown that for function f with certain smoothness properties at the ends of interval [−1, 1] the rate of weighted approximation by Vallee- Poussin means has the same order as the best weighted approximation of f.