Lambert W Function for Applications in Physics

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. Program summary Program title: LambertW Catalogue identifier: AENC_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENC_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 1335 No. of bytes in distributed program, including test data, etc.: 25 283 Distribution format: tar.gz Programming 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 MB Classification: 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.

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