Modified Gauss–Laguerre Exponential Fitting Based Formulae

Modified Gauss–Laguerre exponentially fitted quadrature rules are introduced for the computation of integrals of oscillatory functions over the whole positive semiaxis. Their weights and nodes depend on the frequency of oscillation in the integrand, thus increasing the accuracy of classical Gauss–Laguerre formulae. The asymptotic order is discussed, and an algorithm for determining weights and nodes for a general number N of nodes is provided, resulting an improvement of the existing quadrature formulae. Numerical illustrations are also presented.