Lambert $W$-Function Branch Identities
Complex Variables
2021-01-19 v2 Combinatorics
Abstract
After defining in detail the Lambert -function branches, we give a large number of exact identities involving (infinite) symmetric functions of these branches, as well as geometrically convergent series for all the branches. In doing so, we introduce a family of polynomials which may be of independent interest.
Cite
@article{arxiv.2012.11698,
title = {Lambert $W$-Function Branch Identities},
author = {Henri Cohen},
journal= {arXiv preprint arXiv:2012.11698},
year = {2021}
}
Comments
Added appendix by Letong Hong and Shengton Zhang finishing the proof of Theorem 3.3