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arXiv · 2306.16362

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

Per Åhag·Rafał Czyż·Per-Håkan Lundow
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Abstract

The $\psi(x)$-function, which solves the equation $x = \sinh(aw)e^w$ 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 give 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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Per Åhag, Rafał Czyż, Per-Håkan Lundow. 2023-06-28. Complex branches of a generalised Lambert $W$ function arising from $p,q$--binomial coefficients. https://doi.org/10.4064/ap240830-1-7

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