DRAFT: Integration of oscillatory integrals, a computer-algebra approach

The numerical integration of oscillatory integrals is an important and well-studied area of mathematical inquiry. See [11] for a series of recent conferences on the topic, including applications. Examining some of the proffered methods from the position of a computer algebra system (CAS) provides several opportunities not available with purely numerical approaches. Given an explicit representation of the integrand in symbolic form, one can consider use use of symbolic derivatives of components as part of the processing. Additionally, one may utilize a framework for error control based on exact or arbitrarilyhigh-precision arithmetic. A CAS may provide for simple exposition upon which further elaborations may be built. By executing code in a symbolic system it is also possible to compute approximate answers as expressions in terms of symbolic parameters such as frequency, displaying the nature of dependencies as well as re-useable formulas for different values of parameters.