Asymptotics of the Humbert Function \(\Psi_1\) for Two Large Arguments

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 fun...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: Peng-Cheng, Hang, Min-Jie Luo
Format: Article
Language:English
Subjects:
Asymptotic properties
Asymptotic series
Hypergeometric functions
Integral transforms
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2403.14942