Efficient Evaluation of Integrals of Analytic Functions by the Trapezoidal Rule

Definite integrals of analytic functions can often be evaluated efficiently by the trapezoidal rule after a suitable transformation. Here the work of Moran 1 and Schwartz 2 along this line is extended. First the dependence of the error on the spacing is discussed, and then several types of transformations are described and applied to integrals of technical interest.