The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis

Abstract

The Euler-MacLaurin summation formula is used to deduce the Whittaker-Shannon sampling theorem for not necessarily band-limited functions, as well as to study numerical integration over the real axis. Concerning the latter, error estimates are determined in case the function to be integrated is smooth but not necessarily analytic. Two characteristic examples are given. © 1983.