Approximation of a function and its derivatives by entire functions

TL;DR

This paper presents a straightforward proof demonstrating that functions with continuous derivatives up to order m on the real line can be approximated, along with their derivatives, by entire functions.

Contribution

It provides a simple proof of a known approximation result for differentiable functions and their derivatives by entire functions.

Findings

Functions with continuous derivatives can be approximated by entire functions.

The approximation includes derivatives up to order m.

The proof simplifies understanding of function approximation by entire functions.

Abstract

A simple proof is given of the known fact that an m-times continuously differentiable function on the real line can be approximated along with its derivatives by an entire function and its respective derivatives.