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 | |
| Publication status | Published - 1 Mar 2019 |
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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 journal › Article
TY - JOUR
T1 - Inequalities and asymptotic expansions related to the volume of the unit ball in Rn
AU - Chen, Chao Ping
AU - Paris, Richard B.
PY - 2019/3/1
Y1 - 2019/3/1
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.
AB - 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.
U2 - 10.1007/s00025-019-0967-1
DO - 10.1007/s00025-019-0967-1
M3 - Article
VL - 74
JO - Results in Mathematics
T2 - Results in Mathematics
JF - Results in Mathematics
SN - 1422-6383
IS - 1
M1 - 44
ER -