A class of functions for which the trapezoidal rule gives the exact value of integral over the infinite interval

摘要

The problem of finding a class of functions for which the trapezoidal rule gives the exact value of the improper integral over the infinite interval (− ∞, + ∞) is considered. Specifically, it is shown that, for an entire function of exponential type A, the trapezoidal rule with mesh size h < 2π/A gives the exact value of the improper integral over (− ∞, + ∞). This is an improvement of Boas and Pollard's result.