THE NUMERICAL EVALUATION OF A CLASS OF SINGULAR, OSCILLATORY INTEGRALS

Two methods are presented to evaluate integrands with oscillatory inte grals which have specific singularities. The first method is valid for oscillatory frequencies less than 1000, and is based on the method of Piessens and Poleunis in which the oscillatory factor is expanded as a series of Bessel functions. For large frequencies an asymptotic meth od based on expansions of Erdelyi is used. Singularities of the form ( 1-x)alpha ln(1-x)(s)(1+x)(beta)ln(1+x)(t) can be handled on the interv al [-1,1]. A selection of practical examples is evaluated to demonstra te the procedures.