Analytic functions, also known as holomorphic functions, form the cornerstone of complex analysis, widely studied for their elegant properties and deep connections in both pure and applied ...

In a previous paper (Lyness and Moler [1]), several closely related formulas of use for obtaining a derivative of an analytic function numerically are derived. Each of these formulas consists of a ...

It is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions. To avoid instability, one must settle for ...