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. These formulas were derived by combining the Sinc approximation with appropriate conformal maps. It has been demonstrated that these 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 a theoretical error analysis and numerical experiments that confirm the effectiveness of our new formulas.