Rational approximation to the Thomas--Fermi equation

TL;DR

This paper introduces a simple rational approximation method for the Thomas--Fermi equation that achieves highly accurate slope calculations at the origin, outperforming existing approaches.

Contribution

It presents a novel rational approximation technique that significantly improves the accuracy of the slope at the origin for the Thomas--Fermi equation.

Findings

Unprecedented accuracy in the slope at the origin.

Comparison shows superiority over other methods.

Simplifies the approximation process.

Abstract

We show that a simple and straightforward rational approximation to the Thomas--Fermi equation provides the slope at origin with unprecedented accuracy. We compare present approach with other available ones.