Proceedings of the 2019 Undergraduate Mathematics Day
Manipulations of Taylor series expansions of increasing numbers of terms yield finite difference approximations of derivatives with increasing rates of convergence. In this paper, we consider central difference approximations of arbitrary order of accuracy. We derive explicit formulas for the weights of terms and explore their limits for increasing orders of accuracy.
Finite Difference formulas, first derivative
Boorsma, Preston R., "Analysis of Weights in Central Difference Formulas for Approximation of the First Derivative" (2020). Undergraduate Mathematics Day: Proceedings and Other Materials. 37.