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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