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

SDI

Research output: Contribution to journal › Article

19 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

Fingerprint Dive into the research topics of 'Inequalities and asymptotic expansions related to the volume of the unit ball in R<sup>n</sup>'. Together they form a unique fingerprint.

Cite this

Chen, C. P., & Paris, R. B. (2019). Inequalities and asymptotic expansions related to the volume of the unit ball in Rⁿ. Results in Mathematics, 74(1), [44]. https://doi.org/10.1007/s00025-019-0967-1

@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 -