  We introduce a new type of cubature formula for the evaluation of an integral
over the disk with respect to a weight function. The method is based on an
analysis of the Fourier series of the weight function and a reduction of the
bivariate integral into an infinite sum of univariate integrals. Several
experimental results show that the accuracy of the method is superior to
standard cubature formula on the disk. Error estimates provide the theoretical
basis for the good performance of the new algorithm.
