A new general asymptotic formula and inequalities involving the volume of the unit ball

JOURNAL OF NUMBER THEORY

卷:170

Article

Lu, Dawei^1,2  Zhang, Peixuan¹ 

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116023, Peoples R China

[2] Chinese Univ Hong Kong, Dept Stat, Shatin, Hong Kong, Peoples R China

关键词: Gamma function;    Continued fraction;    Rate of convergence;    The volume of the unit;    n-dimensional ball;    Inequalities;    Asymptotic formula;   

DOI  :  10.1016/j.jnt.2016.06.010

来源: Elsevier

【 摘 要 】

In this paper, based on some early works, we establish a general continued fraction approximation for the nth root of the volume of the unit n-dimensional ball. Then related inequalities are given. Finally, for demonstrating the superiority of our new estimates and inequalities, we present some numerical computations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free