# New conformal map for the Sinc approximation for exponentially decaying functions over the semi-infinite interval

## TL;DR

This paper introduces a new conformal map tailored for the Sinc approximation of exponentially decaying functions on semi-infinite intervals, enhancing convergence rates through theoretical and numerical validation.

## Contribution

The paper proposes a novel conformal map specifically designed for semi-infinite, exponentially decaying functions, improving the efficiency of the Sinc approximation.

## Key findings

- Improved convergence rate demonstrated theoretically.
- Numerical experiments confirm enhanced performance.
- New conformal map outperforms existing maps.

## Abstract

The Sinc approximation has shown high efficiency for numerical methods in many fields. Conformal maps play an important role in the success, i.e., appropriate conformal map must be employed to elicit high performance of the Sinc approximation. Appropriate conformal maps have been proposed for typical cases; however, such maps may not be optimal. Thus, the performance of the Sinc approximation may be improved by using another conformal map rather than an existing map. In this paper, we propose a new conformal map for the case where functions are defined over the semi-infinite interval and decay exponentially. Then, we demonstrate in both theoretical and numerical ways that the convergence rate is improved by replacing the existing conformal map with the proposed map.