Gaussian quadrature rules with an exponential weight on the real semiaxis

Abstract

We consider some “truncated” Gaussian rules based on the zeros of the orthonormal polynomials w.r.t. the weight function w(x) = e−x −α−xβ with x ∈ (0,+∞), α > 0 and β > 1. We show that these formulas are stable and converge with the order of the best polynomial approximation in suitable function spaces. Moreover, we apply these results to the related Lagrange interpolation process in weighted L spaces. Finally, some numerical tests are shown.