Exponentially fitted quadrature rules of Gauss type for oscillatory integrands

We consider the construction of N-point exponential fitted quadrature rules. Whereas the classical quadrature rules are constructed upon only polynomial considerations, the newly constructed rules will take into account both polynomial and exponential aspects. This leads to a variety of rules with interesting features. In particular we will investigate the possible application of these rules to highly oscillatory integrands. This is illustrated for N⩽4.