Reply to the Comment on ‘Improving series convergence: the simple pendulum and beyond’

Abstract

Abstract We correct an error pointed out by a reader in an example included in a previous article about a method for improving series convergence. After the correction, the conclusion of the previous article, that the method reduces the number of terms needed to achieve a desired accuracy, remains true. We clarify that when the evaluation of an integral requires a series expansion, we measure the speed of convergence by the inverse of the number of terms required to achieve a certain accuracy. In most cases, fewer terms will mean less computational expense. We provide an additional example to emphasize the generality of the method in the previous article.