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arXiv · 2501.07281

Asymptotics of the Humbert functions $\Psi_1$ and $\Psi_2$

Peng-Cheng Hang·Malte Henkel·Min-Jie Luo
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Abstract

A compilation of new results on the asymptotic behaviour of the Humbert functions $\Psi_1$ and $\Psi_2$, and also on the Appell function $F_2$, is presented. As a by-product, we confirm a conjectured limit which appeared recently in the study of the $1D$ Glauber-Ising model. We also propose two elementary asymptotic methods and confirm through some illustrative examples that both methods have great potential and can be applied to a large class of problems of asymptotic analysis. Finally, some directions of future research are pointed out in order to suggest ideas for further study.

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Peng-Cheng Hang, Malte Henkel, Min-Jie Luo. 2025-01-13. Asymptotics of the Humbert functions $\Psi_1$ and $\Psi_2$. https://doi.org/10.1016/j.jat.2025.106233

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