Modified SE-Sinc approximation with boundary treatment over the semi-infinite interval and its error bound

Abstract

The Sinc approximation is known as an efficient function approximation formula for functions that decay exponentially and are defined over the entire infinite interval. Even for functions that do not satisfy such conditions, Stenger constructed an approximation formula based on the Sinc approximation combining with the Single-Exponential (SE) transformation and introducing auxiliary basis functions. In this study, we improve the approximation formula by replacing the SE transformation and the auxiliary basis functions. Two kinds of error bounds for the modified formula are also given.