F. Stenger proposed efficient approximation formulas for derivatives over infinite intervals. Those formulas were derived by the combination of the Sinc approximation and appropriate conformal maps. It has been shown that those formulas can attain root-exponential convergence. In this study, we enhance the convergence rate by improving the conformal maps employed in those formulas. We provide theoretical error analysis and numerical experiments that confirm the effectiveness of our new formulas.

翻译：F. Stenger 提出了针对无限区间上导数的高效近似公式。这些公式通过结合 Sinc 逼近与适当的共形映射推导得出。已有研究表明，这些公式能够达到根指数级收敛。在本研究中，我们通过改进这些公式中所使用的共形映射，提升了其收敛速度。我们提供了理论误差分析及数值实验，验证了我们新公式的有效性。