Sharp approximation formulas and inequalities for the Wallis ratio by continued fraction

Xu You; Di Rong Chen

doi:10.1016/j.jmaa.2017.06.063

Sharp approximation formulas and inequalities for the Wallis ratio by continued fraction

Xu You^*
, Di Rong Chen

^*Corresponding author for this work

School of Mathematical Sciences

Beijing Institute of Petrochemical Technology
Wuhan Textile University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we present a new continued fraction approximation of the Wallis ratio. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation.

Original language	English
Pages (from-to)	1743-1748
Number of pages	6
Journal	Journal of Mathematical Analysis and Applications
Volume	455
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2017.06.063
State	Published - 15 Nov 2017

Keywords

Gamma function
Inequalities
Multiple-correction method
Wallis ratio

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10.1016/j.jmaa.2017.06.063

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title = "Sharp approximation formulas and inequalities for the Wallis ratio by continued fraction",

abstract = "In this paper, we present a new continued fraction approximation of the Wallis ratio. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation.",

keywords = "Gamma function, Inequalities, Multiple-correction method, Wallis ratio",

author = "Xu You and Chen, \{Di Rong\}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = nov,

day = "15",

doi = "10.1016/j.jmaa.2017.06.063",

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TY - JOUR

T1 - Sharp approximation formulas and inequalities for the Wallis ratio by continued fraction

AU - You, Xu

AU - Chen, Di Rong

PY - 2017/11/15

Y1 - 2017/11/15

N2 - In this paper, we present a new continued fraction approximation of the Wallis ratio. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation.

AB - In this paper, we present a new continued fraction approximation of the Wallis ratio. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation.

KW - Gamma function

KW - Inequalities

KW - Multiple-correction method

KW - Wallis ratio

UR - https://www.scopus.com/pages/publications/85021651289

U2 - 10.1016/j.jmaa.2017.06.063

DO - 10.1016/j.jmaa.2017.06.063

M3 - 文章

AN - SCOPUS:85021651289

SN - 0022-247X

VL - 455

SP - 1743

EP - 1748

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Sharp approximation formulas and inequalities for the Wallis ratio by continued fraction

Abstract

Keywords

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