English

Complex branches of a generalised Lambert $W$ function arising from $p,q$--binomial coefficients

Complex Variables 2023-11-28 v2 Statistical Mechanics Classical Analysis and ODEs

Abstract

The ψ(x)\psi(x)-function, which solves the equation x=sinh(aw)ewx = \sinh(aw)e^w for 0<a<10<a<1, has a natural connection to the renowned Lambert WW function and also physical relevance through its connection to the Lenz-Ising model of ferromagnetism. We give a detailed analysis of its complex branches and construct Riemann surfaces from these under various conditions of aa, unveiling intriguing new links to the Lambert WW function.

Keywords

Cite

@article{arxiv.2306.16362,
  title  = {Complex branches of a generalised Lambert $W$ function arising from $p,q$--binomial coefficients},
  author = {Per Åhag and Rafał Czyż and Per-Håkan Lundow},
  journal= {arXiv preprint arXiv:2306.16362},
  year   = {2023}
}
R2 v1 2026-06-28T11:17:05.809Z