Lambert W function for applications in physics

The Lambert W(x)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.Program summaryProgram title: LambertWCatalogue identifier: AENC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENC_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License version 3No. of lines in distributed program, including test data, etc.: 1335No. of bytes in distributed program, including test data, etc.: 25 283Distribution format: tar.gzProgramming language: C++ (with suitable wrappers it can be called from C, Fortran etc.), the supplied command-line utility is suitable for other scripting languages like sh, csh, awk, perl etc.Computer: All systems with a C++ compiler.Operating system: All Unix flavors, Windows. It might work with others.RAM: Small memory footprint, less than 1 MBClassification: 1.1, 4.7, 11.3, 11.9.Nature of problem:Find fast and accurate numerical implementation for the Lambert W function.Solution method:Halley’s and Fritsch’s iterations with initial approximations based on branch-point expansion, asymptotic series, rational fits, and continued logarithm recursion.Additional comments:Distribution file contains the command-line utility lambert-w. Doxygen comments, included in the source files. Makefile.Running time:The tests provided take only a few seconds to run.