Improvement of conformal maps combined with the Sinc approximation for derivatives over infinite intervals

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.