  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.
