Peng-Cheng Hang

activity

20242026

collaborators

8 papers

math.CA2026

Fourier transform pairs and Eisenstein-type series related to Jacobi elliptic functions

Peng-Cheng Hang, Alexey Kuznetsov

We compute Fourier transforms of functions expressed as a ratio of one of the Jacobi elliptic functions divided by $sinh (I ¨ x)$ or $cosh (I ¨ x)$ . In many cases, the resulting Fourie…

math.CA2026

Asymptotic expansions of the Humbert Function $I^¦_{1}$ and their applications

Peng-Cheng Hang, Liangjian Hu, Min-Jie Luo

This paper systematically studies the asymptotics of Humbert's bivariate confluent hypergeometric function $I^¦_{1} [a, b; c; x, y]$ . Specifically, we establish explicit asymptotic expans…

math.CA2025

Complete asymptotic expansions of the Humbert function $I^¨_{1}$ for two large arguments

Peng-Cheng Hang, Liangjian Hu, Min-Jie Luo

In our recent work [SIGMA \textbf{20} (2024), 074, 13 pages], the leading behaviour of the Humbert function $I^¨_{1} [a, b; c, c^{'}; x, y]$ when $x \to \infty$ and $y \to + \infty$ has been deriv…

math.CA2025

Asymptotics of the Humbert functions $I^¨_{1}$ and $I^¨_{2}$

Peng-Cheng Hang, Malte Henkel, Min-Jie Luo

A compilation of new results on the asymptotic behaviour of the Humbert functions $I^¨_{1}$ and $I^¨_{2}$ , and also on the Appell function $F_{2}$ , is presented. As a by-product, we confir…

math.NT2024

Note on the $a$ -points of the Riemann zeta function

Peng-Cheng Hang, Min-Jie Luo

For any $a \in C$ , the zeros of $I^¶ (s) - a$ , denoted by $I ¨ _{a} = I^_{a}^{2} + i I^_{a}^{3}$ , are called $a$ -points of the Riemann zeta function $I^¶ (s)$ . In this paper, we reformulate some basic…

math.CA2024

Asymptotics of the Humbert Function $I^¨_{1}$ for Two Large Arguments

Peng-Cheng Hang, Min-Jie Luo

Recently, Wald and Henkel (2018) derived the leading-order estimate of the Humbert functions $I^¦_{2}$ , $I^¦_{3}$ and $I^_{2}$ for two large arguments, but their technique cannot handle th…

Fourier transform pairs and Eisenstein-type series related to Jacobi elliptic functions

Asymptotic expansions of the Humbert Function I^¦1​ and their applications

Complete asymptotic expansions of the Humbert function I^¨1​ for two large arguments

Asymptotics of the Humbert functions I^¨1​ and I^¨2​

Note on the a-points of the Riemann zeta function

Asymptotics of the Humbert Function I^¨1​ for Two Large Arguments

Asymptotic expansions of the Humbert Function $I^¦_{1}$ and their applications

Complete asymptotic expansions of the Humbert function $I^¨_{1}$ for two large arguments

Asymptotics of the Humbert functions $I^¨_{1}$ and $I^¨_{2}$

Note on the $a$ -points of the Riemann zeta function

Asymptotics of the Humbert Function $I^¨_{1}$ for Two Large Arguments