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

52 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

Access to Document

10.1007/s00025-019-0967-1

Paris_InequalitiesAndAsymptotic_Accepted_2018Accepted author manuscript, 395 KB

Cite this

@article{0323ee9b404c496c8c63b01007ed96dc,

title = "Inequalities and asymptotic expansions related to the volume of the unit ball in Rn",

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.",

author = "Chen, {Chao Ping} and Paris, {Richard B.}",

year = "2019",

month = mar,

day = "1",

doi = "10.1007/s00025-019-0967-1",

language = "English",

volume = "74",

journal = "Results in Mathematics",

issn = "1422-6383",

publisher = "Birkhauser Verlag Basel",

number = "1",

}

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

AN - SCOPUS:85060848329

VL - 74

JO - Results in Mathematics

JF - Results in Mathematics

SN - 1422-6383

IS - 1

M1 - 44

ER -

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

Abstract

Access to Document

Fingerprint

Cite this

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