New Bounds and Asymptotic Expansions for the Volume of the Unit Ball in Rn Based on Pade Approximation

被引：0

作者：

Zhang, Huijie ^{[1
]}

机构：

[1] Univ Shanghai Sci & Technol, Business Sch, Shanghai 200093, Peoples R China

来源：

RESULTS IN MATHEMATICS | 2022年 / 77卷 / 03期

关键词：

Volume of the unit n-dimensional ball; gamma function; inequality; asymptotic expansion; pade approximation; INEQUALITIES; GAMMA; FORMULA;

D O I：

10.1007/s00025-022-01652-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Omega(n )= pi(n/2)/Gamma(n/2 + 1)(n is an element of N) denote the volume of the unit ball in R-n. In this paper, we present asymptotic expansions and new bound related to the quantities: Omega(n)/Omega(n-1) and Omega(2)(n)/Omega(n-1)Omega(n+1). Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed method.

引用

页数：15

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