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The Lambert W Function on the Reals
| Title: | The Lambert W Function on the Reals |
| Author: | Manuel Eberl |
| Submission date: | 2020-04-24 |
| Abstract: |
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. |
| BibTeX: |
@article{Lambert_W-AFP,
author = {Manuel Eberl},
title = {The Lambert W Function on the Reals},
journal = {Archive of Formal Proofs},
month = apr,
year = 2020,
note = {\url{http://isa-afp.org/entries/Lambert_W.html},
Formal proof development},
ISSN = {2150-914x},
}
|
| License: | BSD License |
| Depends on: | Bernoulli, Stirling_Formula |
| Status: [ok] | This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations. |
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