Peng-Cheng Hang

activity

20242026

most citedAsymptotics of the Humbert functions

Ψ_{1}

and

Ψ_{2}

1 citations · 2 across the 8 of their papers we have counts for

collaborators

9 papers

math.CA2026

Equal-Phase Monotonicity for Weighted Jacobi-Radau Functions and Jacobi Lebesgue Constants

K. Castillo, P. -C. Hang

For the Jacobi family with parameters $(0, β)$ , $β \geq - 1/3$ , we prove a continuous comparison theorem for the associated weighted Jacobi--Radau functions. When two consecutive funct…

math.CA2025

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 $sinh (π x)$ or $cosh (π x)$ . In many cases, the resulting Fourier…

math.CA2025

Asymptotic expansions of the Humbert Function $Φ_{1}$ and their applications

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

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

math.CA2025★ 1 cited

Asymptotics of the Humbert functions $Ψ_{1}$ and $Ψ_{2}$

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

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

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 $ζ (s) - a$ , denoted by $ρ_{a} = β_{a} + i γ_{a}$ , are called $a$ -points of the Riemann zeta function $ζ (s)$ . In this paper, we reformulate some basic resu…

math.CA2024

Complete asymptotic expansions of the Humbert function $Ψ_{1}$ 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 $Ψ_{1} [a, b; c, c^{'}; x, y]$ when $x \to \infty$ and $y \to + \infty$ has been derive…

math.CA2024

Asymptotics of Saran's hypergeometric function $F_{K}$

Peng-Cheng Hang, Min-Jie Luo

In this paper, we first establish asymptotic expansions of the Humbert function $Ψ_{1}$ for one large variable. The resulting expansions are then used to derive an asymptotic expansi…

math.CA2024

Matrix analogues of some asymptotic methods for Laplace integrals

Peng-Cheng Hang

The matrix analogues of Laplace's method and Watson's lemma are derived via the approach described by Williams and Wong [J. Approx. Theory 24 (4) (1974), 378-384]. Some examples ar…

math.CA2024★ 1 cited

Asymptotics of the Humbert Function $Ψ_{1}$ for Two Large Arguments

Peng-Cheng Hang, Min-Jie Luo

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

Equal-Phase Monotonicity for Weighted Jacobi-Radau Functions and Jacobi Lebesgue Constants

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

Asymptotic expansions of the Humbert Function Φ1​ and their applications

Asymptotics of the Humbert functions Ψ1​ and Ψ2​

Note on the a-points of the Riemann zeta function

Complete asymptotic expansions of the Humbert function Ψ1​ for two large arguments

Asymptotics of Saran's hypergeometric function FK​

Matrix analogues of some asymptotic methods for Laplace integrals

Asymptotics of the Humbert Function Ψ1​ for Two Large Arguments

Asymptotic expansions of the Humbert Function $Φ_{1}$ and their applications

Asymptotics of the Humbert functions $Ψ_{1}$ and $Ψ_{2}$

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

Complete asymptotic expansions of the Humbert function $Ψ_{1}$ for two large arguments

Asymptotics of Saran's hypergeometric function $F_{K}$

Asymptotics of the Humbert Function $Ψ_{1}$ for Two Large Arguments