A numerical evaluation of integrals by the method of steepest descents Original Research Article

In 1987, Campbell, Fröman and Walles [1] gave an explicit series formula for the evaluation of integrals by the method of steepest descents, the formula being programmed for the symbolic computing system REDUCE. In this paper, we present a direct computation of the coefficients of the asymptotic expansions of these integrals, based on Cauchyʹs formula, and the Hermite corrector formula [2].