Approximation by Power Series of Functions

TL;DR

This paper introduces a method for constructing derivative-matching approximations using power series derived from functions, leveraging Bell polynomials, with potential applications in numerical mathematics.

Contribution

It presents a novel approach to approximation using power series and Bell polynomials, expanding tools available for numerical analysis.

Findings

Developed a new power series approximation method.

Utilized Bell polynomials for derivative matching.

Potential applications in numerical mathematics identified.

Abstract

Derivative-matching approximations are constructed as power series built from functions. The method assumes the knowledge of special values of the Bell polynomials of the second kind, for which we refer to the literature. The presented ideas may have applications in numerical mathematics.