On optimal convergence rates of Laguerre polynomial expansions for piecewise functions

Abstract

By applying Hilb type formula and generalized van der Corput type Lemmas, this paper presents optimal decay rates on the expansion coefficients for given functions expanded in the form of Laguerre polynomial series, from which it leads to the convergence rates on the spectral orthogonal projections, and derives new estimates on the errors for Gauss–Laguerre quadrature. Ample numerical experiments are carried out to validate the optimality and accuracy of these theoretical results.