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

^*此作品的通讯作者

数学科学学院

Beijing Institute of Petrochemical Technology
Wuhan Textile University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
页（从-至）	1743-1748
页数	6
期刊	Journal of Mathematical Analysis and Applications
卷	455
期	2
DOI	https://doi.org/10.1016/j.jmaa.2017.06.063
出版状态	已出版 - 15 11月 2017

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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",

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

AU - You, Xu

AU - Chen, Di Rong

PY - 2017/11/15

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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

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