Email Gateway (Aug 23 2022 at 08:50): Email Gateway (Aug 23 2022 at 08:50):From: Lawrence Paulson <lp15@cam.ac.uk>
I’m happy to announce yet another AFP entry: The Lambert W Function on the Reals, by Manuel Eberl. It builds on a tower of Manuel’s other contributions.
The Lambert W function is a multi-valued function defined as the inverse function of x ↦ x ex. Besides numerous applications in combinatorics, physics, and engineering, it also frequently occurs when solving equations containing both ex and x, or both x and log x.
This article provides a definition of the two real-valued branches W0(x) and W-1(x) and proves various properties such as basic identities and inequalities, monotonicity, differentiability, asymptotic expansions, and the MacLaurin series of W0(x) at x = 0.
You’ll find it online at https://www.isa-afp.org/entries/Lambert_W.html
Larry
Last updated: Nov 21 2024 at 12:39 UTC