Lambert W-Function Branch Identities

2020/12/21 by Henri Cohen, Cohen, Henri
Engineering · Mathematics · Physics and Astronomy · #05A10 (Secondary) #30D15 (Primary) 30E15 #Combinatorics (math.CO) #Complex Variables (math.CV) #Experimental and Theoretical Physics Studies #FOS: Mathematics #Sports Dynamics and Biomechanics #math.CO #math.CV #msc:05A10 #msc:30D15 #msc:30E15

paper · pdf · doi:10.48550/arxiv.2012.11698

Added appendix by Letong Hong and Shengton Zhang finishing the proof of Theorem 3.3

openalex publication_date 2020/12/21 · arxiv created 2021/01/18 · arxiv updated 2021/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

After defining in detail the Lambert W-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.

Related

• On the generalization of the Lambert W function with applications in theoretical physics
• Another Incarnation of the Lambert W Function
• Complex branches of a generalised Lambert W function arising from p,q--binomial coefficients
• A catalog of interesting and useful Lambert series identities
• Unimodal sequences show Lambert W is Bernstein