Numerical quadrature for integrals involving oscillating functions

This paper deals with the construction of a coupled Gaussian rule for weight functionsinvolving powers, exponentials and trigonometric functions. Starting from a recursive rela-tion for the moments, nodes and weights are computed by using the Chebyshev algorithmtogether with the Golub and Welsch method. An a posteriori approximation of the quadra-ture error by means of the generalized averaged Gaussian rules is also considered. Severalnumerical examples are provided.