  While the trapezoidal formula can attain exponential convergence when applied
to infinite integrals of bilateral rapidly decreasing functions, it is not
capable of this in the case of unilateral rapidly decreasing functions. To
address this issue, Stenger proposed the application of a conformal map to the
integrand such that it transforms into bilateral rapidly decreasing functions.
Okayama and Hanada modified the conformal map and provided a rigorous error
bound for the modified formula. This paper proposes a further improved
conformal map, with two rigorous error bounds provided for the improved
formula. Numerical examples comparing the proposed and existing formulas are
also given.
