Extrapolation Methods for Oscillatory Infinite Integrals

The non-linear transformations for accelerating the convergenceof slowly convergent infinite integrals due to Levin & Sidi(1975) are modified in two ways. These modifications enableone to evaluate accurately some oscillatory infinite integralswith less work. Special emphasis is placed on the evaluationof Fourier and Hankel transforms and some simple algorithmsfor them are given. Convergence properties of these modificationsare analysed in some detail and powerful convergence theoremsare proved for certain cases including those of the Fourierand Hankel transforms treated here. Several numerical examplesare also supplied.