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Asymptotics of the Humbert Function $\Psi_1$ for Two Large Arguments
Peng-Cheng Hang, Min-Jie Luo Department of Mathematics, School of Mathematics and Statistics, Donghua University, Shanghai 201620, P.R. China
Аннотация:
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.
Ключевые слова:
Humbert function, asymptotics, generalized hypergeometric function.
Поступила: 27 марта 2024 г.; в окончательном варианте 2 августа 2024 г.; опубликована 9 августа 2024 г.
Образец цитирования:
Peng-Cheng Hang, Min-Jie Luo, “Asymptotics of the Humbert Function $\Psi_1$ for Two Large Arguments”, SIGMA, 20 (2024), 074, 13 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma2076 https://www.mathnet.ru/rus/sigma/v20/p74
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