Improvement of the conformal map combined with the Sinc approximation for unilateral rapidly decreasing functions

Abstract

The Sinc approximation is very efficient for bilateral rapidly decreasing functions. Even for non-bilateral rapidly decreasing functions, the Sinc approximation can work accurately if combined with an appropriate conformal map. Appropriate conformal maps for typical cases have been proposed in the literature. In the case of unilateral rapidly decreasing functions, however, it can be improved further. In this paper, we employ an improved conformal map for the case of unilateral rapidly decreasing functions. In addition, we present a computable error bound for the improved approximation formula.