Min-Jie Luo

activity

20242026

collaborators

6 papers

math.GM2026

Multivariate Laguerre polynomials: new results and insights

Liang-Jia Guo, Min-Jie Luo, Ravinder Krishna Raina +1

In this paper, we study various properties of ErdÃ©lyi's multivariate Laguerre polynomials $L_{n_{1}, \dots, n_{k}}^{(I^\pm)} (x_{1}, \dots, x_{k})$ including their generating functions, product…

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…

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 $I^¨_{1}$ for one large variable. The resulting expansions are then used to derive an asymptotic expans…

Multivariate Laguerre polynomials: new results and insights

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

Asymptotics of Saran's hypergeometric function FK​

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

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