Inequalities and asymptotic expansions related to the volume of the unit ball in Rn

Chao Ping Chen; Richard B. Paris

doi:10.1007/s00025-019-0967-1

Inequalities and asymptotic expansions related to the volume of the unit ball in Rⁿ

Chao Ping Chen^*, Richard B. Paris

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

112 Downloads (Pure)

Abstract

Let Ωn=πn/2/Γ(n2+1)(n∈N)Ωn=πn/2/Γ(n2+1)(n∈N) denote the volume of the unit ball in RnRn. In this paper, we present asymptotic expansions and inequalities related to ΩnΩn and the quantities:

Ωn−1Ωn,ΩnΩn−1+Ωn+1andΩ1/nnΩ1/(n+1)n+1.

Original language	English
Article number	44
Number of pages	28
Journal	Results in Mathematics
Volume	74
Issue number	1
Early online date	31 Jan 2019
DOIs	https://doi.org/10.1007/s00025-019-0967-1
Publication status	Published - 1 Mar 2019

Keywords

Volume of the unit n-dimensional ball
Gamma function
Asymptotic expansions
Inequalities

Access to Document

10.1007/s00025-019-0967-1

Paris_InequalitiesAndAsymptotic_Accepted_2018Accepted author manuscript, 395 KB

Cite this

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abstract = "Let Ωn=πn/2/Γ(n2+1)(n∈N)Ωn=πn/2/Γ(n2+1)(n∈N) denote the volume of the unit ball in RnRn. In this paper, we present asymptotic expansions and inequalities related to ΩnΩn and the quantities:Ωn−1Ωn,ΩnΩn−1+Ωn+1andΩ1/nnΩ1/(n+1)n+1.",

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