Differentiation Formulas for Analytic Functions

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Abstract
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 convergent series, each term being a sum of function evaluations in the complex plane. In this paper we introduce a simple generalization of the previous methods; we investigate the "truncation error" associated with truncating the infinite series. Finally we recommend a particular differentiation rule, not given in the previous paper.

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