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arXiv · 2403.14942

Asymptotics of the Humbert Function $\Psi_1$ for Two Large Arguments

Peng-Cheng Hang·Min-Jie Luo
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Abstract

Recently, Wald and Henkel (2018) derived the leading-order estimate of the Humbert functions $\Phi_2$, $\Phi_3$ and $\Xi_2$ for two large arguments, but their technique cannot handle the Humbert function $\Psi_1$. In this paper, we establish the leading asymptotic behavior of the Humbert function $\Psi_1$ for two large arguments. Our proof is based on a connection formula of the Gauss hypergeometric function and Nagel's approach (2004). This approach is also applied to deduce asymptotic expansions of the generalized hypergeometric function $_pF_q$ $(p\leqslant q)$ for large parameters, which are not contained in NIST handbook.

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Peng-Cheng Hang, Min-Jie Luo. 2024-03-22. Asymptotics of the Humbert Function $\Psi_1$ for Two Large Arguments. https://doi.org/10.3842/sigma.2024.074

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