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

Chao Ping Chen, Richard B. Paris

Research output: Contribution to journalArticle

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.
LanguageEnglish
Article number44
Number of pages28
JournalResults in Mathematics
Volume74
Issue number1
Early online date31 Jan 2019
DOIs
Publication statusE-pub ahead of print - 31 Jan 2019

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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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Inequalities and asymptotic expansions related to the volume of the unit ball in Rn. / Chen, Chao Ping; Paris, Richard B.

In: Results in Mathematics, Vol. 74, No. 1, 44, 01.03.2019.

Research output: Contribution to journalArticle

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AU - Paris, Richard B.

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N2 - 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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JF - Results in Mathematics

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