Asymptotics of the Humbert functions Ψ1 and Ψ2

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2025-09-03 DOI:10.1016/j.jat.2025.106233

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

引用次数: 0

Abstract

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 a conjectured limit which appeared recently in the study of the

1 D

Glauber–Ising model. We also propose two elementary asymptotic methods and confirm through some illustrative examples that both methods have great potential and can be applied to a large class of problems of asymptotic analysis. Finally, some directions of future research are pointed out in order to suggest ideas for further study.

查看原文本刊更多论文

Humbert函数的渐近性Ψ1和Ψ2

本文给出了关于Humbert函数Ψ1和Ψ2以及apell函数F2渐近行为的新结果汇编。作为一个副产品，我们证实了最近在一维格劳伯-伊辛模型研究中出现的一个推测极限。我们还提出了两种初等渐近方法，并通过一些例子证实了这两种方法都有很大的潜力，可以应用于大量的渐近分析问题。最后，对今后的研究方向进行了展望，为今后的研究提供思路。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.