Error estimates with explicit constants for the Sinc approximation over infinite intervals

Abstract

The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation works accurately when combined with a proper variable transformation. The convergence rate has been analyzed for typical cases including finite, semi-infinite, and infinite intervals. Recently, for verified numerical computations, a more explicit, "computable" error bound has been given in the case of a finite interval. In this paper, such explicit error bounds are derived for other cases.