ANALYTICAL AND ASYMPTOTIC REPRESENTATIONS FOR TWO SEQUENCE RELATED TO GAUSS' LEMNISCATE FUNCTIONS

被引：1

作者：

Han, Xue-Feng ^{[1
]}

Chen, Chao-Ping ^{[1
]}

Srivastava, H. M. ^{[2
,3
,4
,5
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo 454000, Henan, Peoples R China

[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[3] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[4] Azerbaijan Univ, Dept Math & Informat, 71 Jeyhun Hajibeyli St, Baku AZ-1007, Azerbaijan

[5] Int Telemat Univ Uninettuno, Sect Math, I-00186 Rome, Italy

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2023年 / 17卷 / 02期

关键词：

Gamma and Beta functions; Lemniscate functions; Asymptotic expansions; Zeta functions; Bell polynomials;

D O I：

10.2298/AADM220810024H

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let the sequences G(n) and g(n) be defined by G(n) := integral(1 )(0)dt/(1 - t(2n))(1/n) (n >= 2) and g(n) := integral(infinity )(0)dt/(1 + t(2n))(1/n) (n >= 1). In this paper, we first derive analytical representations for these two sequences G(n) and g(n) in terms of the gamma function. By using the obtained analytical representations, we then deduce asymptotic expansions for G(n) and g(n).

引用

页码：525 / 537

页数：13