|
The
Lambert
W
Function
on
the
Reals
Title: |
The Lambert W Function on the Reals |
Author:
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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{https://isa-afp.org/entries/Lambert_W.html},
Formal proof development},
ISSN = {2150-914x},
}
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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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