An error estimate for the Gauss-Jacobi-Lobatto quadrature rule

Abstract

An error estimate for the Gauss-Lobatto quadrature formula for integration over the interval $[-1,1]$, relative to the Jacobi weight function $w^{\alpha ,\beta }(t)=(1-t{)}^{\alpha }(1+t{)}^{\beta }$, $\alpha ,\beta >-1$, is obtained. This estimate holds true for functions belonging to some Sobolev-type subspaces of the weighted space $L_{w^{\alpha ,\beta }}^1([-1,1])$.

7 pages