Error analysis of approximation of derivatives by means of the Sinc approximation for double-exponentially decaying functions

Abstract

The Sinc approximation is known to yield quite accurate results for double-exponentially decaying functions. To date, this approximation has been successfully applied to derivatives, initial value problems, boundary value problems, and so forth. However, an error analysis of the approximation of the m-th derivatives has not been explicitly given, except in the case of m = 1. This study provides an error analysis for all positive integers m.