Some Quadrature Rules for Finite Trigonometric and Related Integrals

摘要

This article is a partial review of some old work and some new work. Its purpose is to connect up apparently different rules and methods. In particular, an attempt is made to put the Filon Luke rules, the Euler Expansion method, and the Fast Fourier Transform in proper relative perspective to one another. The emphasis here is on the analytical properties of these rules, on how to classify them, and on how to arrange the calculations. There is no discussion of the relative merits of various rules and no error expressions are given.