Lambert W Function for Applications in Physics

TL;DR

This paper explores the Lambert W function's applications in physics and details its numerical implementation in C++ using iterative methods and various initial approximation techniques.

Contribution

It introduces a comprehensive numerical implementation of the Lambert W function tailored for physics applications, combining multiple approximation strategies.

Findings

Efficient C++ implementation of Lambert W function

Use of Halley's and Fritsch's iterations for accuracy

Multiple initial approximation methods improve convergence

Abstract

The Lambert W(x) function and its possible applications in physics are presented. The actual numerical implementation in C++ consists of Halley's and Fritsch's iterations with initial approximations based on branch-point expansion, asymptotic series, rational fits, and continued-logarithm recursion.