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

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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.
Original languageEnglish
Article number44
Number of pages28
JournalResults in Mathematics
Volume74
Issue number1
Early online date31 Jan 2019
DOIs
Publication statusPublished - 1 Mar 2019

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