A new general asymptotic formula and inequalities involving the volume of the unit ball
Release Time:2019-03-12 Hits:
Indexed by: Journal Article
Date of Publication: 2017-01-01
Journal: JOURNAL OF NUMBER THEORY
Included Journals: SCIE
Volume: 170
Page Number: 302-314
ISSN: 0022-314X
Key Words: Gamma function; Continued fraction; Rate of convergence; The volume of the unit; n-dimensional ball; Inequalities; Asymptotic formula
Abstract: 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.