The Sinc approximation is known to be a highly efficient approximation formula for rapidly decreasing functions. For unilateral rapidly decreasing functions, which rapidly decrease as $x\to\infty$ but does not as $x\to-\infty$, an appropriate variable transformation makes the functions rapidly decreasing. As such a variable transformation, Stenger proposed $t = \sinh(\log(\operatorname{arsinh}(\exp x)))$, which enables the Sinc approximation to achieve root-exponential convergence. Recently, another variable transformation $t = 2\sinh(\log(\log(1+\exp x)))$ was proposed, which improved the convergence rate. Furthermore, its computational error bound was provided. However, this improvement was not significant because the convergence rate remained root-exponential. To improve the convergence rate significantly, this study proposes a new transformation, $t = 2\sinh(\log(\log(1+\exp(\pi\sinh x))))$, which is categorized as the double-exponential (DE) transformation. Furthermore, this study provides its computational error bound, which shows that the proposed approximation formula can achieve almost exponential convergence. Numerical experiments that confirm the theoretical result are also provided.

翻译：Sinc逼近已知是快速递减函数的一种高效逼近公式。对于单侧快速递减函数，即当$x\\to\\infty$时快速递减但$x\\to-\\infty$时不递减的情况，适当的变量变换可使函数变为快速递减。作为此类变换，Stenger提出了$t = \\sinh(\\log(\\operatorname{arsinh}(\\exp x)))$，使得Sinc逼近能够实现根指数收敛。最近，另一种变量变换$t = 2\\sinh(\\log(\\log(1+\\exp x)))$被提出，提高了收敛速度，并给出了其计算误差界。然而，由于收敛速度仍保持根指数级，这一改进并不显著。为显著提升收敛速度，本研究提出一种新的变换$t = 2\\sinh(\\log(\\log(1+\\exp(\\pi\\sinh x))))$，该变换属于双指数（DE）变换范畴。此外，本研究提供了其计算误差界，表明所提出的逼近公式可实现几乎指数级的收敛。文中还提供了验证理论结果的数值实验。