English

Lambert $W$-Function Branch Identities

Complex Variables 2021-01-19 v2 Combinatorics

Abstract

After defining in detail the Lambert WW-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.

Keywords

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