On the computation of oscillatory integrals

Computation of integrals of the type is of frequent occurrence in applied problems. Here λ is real and i is the imaginary unit. Tables of the integrals are often required for a wide range of λ values, some of which may be quite large. Tabulation of the integrand for each λ, followed by ordinary methods of numerical integration, is slow and tedious because the number of points required increases with increasing λ. In this paper formulas are given so that once f ( y ) is tabulated over the range of interest, the integral in question can be easily evaluated for any λ.