Lobatto and Radau positive quadrature formulas for linear combinations of Jacobi polynomials

Abstract

For a given $\theta \in (-1,1)$, we find out all parameters $\alpha ,\beta \in \{0,1\}$ such that, there exists a linear combination of Jacobi polynomials $J_{n+1}^{(\alpha ,\beta )}(x)-C{J}_n^{(\alpha ,\beta )}(x)$ which generates a Lobatto (Radau) positive quadrature formula of degree of exactness \textcolor{red}{$2n+2$ ($2n+1$)} and contains the point $\theta$ as a node. These positive quadratures are very useful in studying problems in one-sided polynomial $L_1$ approximation.

arXiv commentThis paper has been withdrawn by the author because a new version has been published in Calcolo