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

Per Åhag; Rafał Czyż; P. H. Lundow

doi:10.4064/ap240830-1-7

August 27, 2025Annales Polonici MathematiciOpen Access

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

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Key Points

The study reveals new connections between the ψ function and the lambert w function, enhancing our understanding of their relationships.
Analysis highlights the construction of riemann surfaces derived from complex branches of the ψ function.
Explores the physical relevance of the ψ function through its link to the lenz ising model, showcasing its application in ferromagnetism.
Investigates the conditions under which these complex branches produce intriguing results, pointing to deeper mathematical contexts.

Implication

This detailed analysis unveils connections between the ψ function and the Lambert W function and construct Riemann surfaces.

Abstract

The ψ(x)-function, which solves the equation x=sinh(aw)ew for 0<a<1, has a natural connection to the renowned Lambert W function and also physical relevance through its connection to the Lenz–Ising model of ferromagnetism. We provide a detailed analysis of its complex branches and construct Riemann surfaces from these under various conditions of a, unveiling intriguing new links to the Lambert W function.

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Cite This Study

Åhag et al. (2025) studied this question.

synapsesocial.com/papers/68c1d5f754b1d3bfb60f9079 https://doi.org/10.4064/ap240830-1-7

View Full Paper

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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