Having Fun with Lambert W(x) Function

TL;DR

This paper introduces the Lambert W(x) function and explores its application in physics, specifically in the context of the Pierre Auger Observatory, including detailed numerical implementation techniques.

Contribution

It provides a practical implementation of Lambert W(x) in C++ and discusses its potential applications in physics research.

Findings

Implementation of Lambert W(x) using Halley's and Fritsch's iteration

Application of Lambert W(x) in physics related to Pierre Auger Observatory

Numerical methods for accurate computation of Lambert W(x)

Abstract

This short note presents the Lambert W(x) function and its possible application in the framework of physics related to the Pierre Auger Observatory. The actual numerical implementation in C++ consists of Halley's and Fritsch's iteration with branch-point expansion, asymptotic series and rational fits as initial approximations.