Representation for the Lagrangian numerical differentiation formula involving elementary symmetric functions

Abstract

By using elementary symmetric functions, this paper presents an explicit representation for the Lagrangian numerical differentiation formula as well as the error estimate for local approximation. And we also point out that the numerical differentiation formula constructed by Li [J.P. Li, General explicit difference formulas for numerical differentiation, J. Comput. Appl. Math. 183 (2005) 29–52] is actually a special case of the Lagrangian numerical differentiation formula to approximate the values of the derivatives at the nodes.