The Lambert W Function on the Reals


Title: The Lambert W Function on the Reals
Author: Manuel Eberl
Submission date: 2020-04-24

The Lambert W function is a multi-valued function defined as the inverse function of xx 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.

  author  = {Manuel Eberl},
  title   = {The Lambert W Function on the Reals},
  journal = {Archive of Formal Proofs},
  month   = apr,
  year    = 2020,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Bernoulli, Stirling_Formula