A quicker approximation of the gamma function towards the Windschitl's formula by continued fraction

被引：0

作者：

Wang, Hongzeng ^{[1
]}

Zhang, Qingling ^{[1
]}

Lu, Dawei ^{[2
]}

机构：

[1] Northeastern Univ, Dept Math, Shenyang 110819, Liaoning, Peoples R China

[2] Dalian Univ Technol, Sch Math Sci, Dalian 116023, Peoples R China

来源：

RAMANUJAN JOURNAL | 2019年 / 48卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Stirling's formula; Windschitl's formula; Continued fraction; Gamma function;

D O I：

10.1007/s11139-017-9974-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish a quicker approximation with continued fraction and some inequalities for the gamma function based on Windschitl's formula. We also give some numerical computations to demonstrate the superiority of our new approximation over the classical ones.

引用

页码：75 / 90

页数：16

共 16 条

[1] On some inequalities for the gamma and psi functions
Alzer, H
[J]. MATHEMATICS OF COMPUTATION, 1997, 66 (217) : 373 - 389
[2] Sharp upper and lower bounds for the gamma function
Alzer, Horst
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2009, 139 : 709 - 718
[3] [Anonymous], 1972, HDB MATH FUNCTIONS F
[4] Burnside W., 1917, Messenger Math, V46, P157
[5] A new continued fraction approximation and inequalities for the Gamma function via the Tri-gamma function
Lu, Dawei
Wang, Xiaoguang
Song, Lixin
Xu, Huiyuan
[J]. RAMANUJAN JOURNAL, 2018, 46 (01) : 119 - 125
[6] A quicker continued fraction approximation of the gamma function related to the Windschitl's formula
Lu, Dawei
Song, Lixin
Ma, Congxu
[J]. NUMERICAL ALGORITHMS, 2016, 72 (04) : 865 - 874
[7] A general asymptotic formula of the gamma function based on the Burnside's formula
Lu, Dawei
Feng, Jinghai
Ma, Cong-Xu
[J]. JOURNAL OF NUMBER THEORY, 2014, 145 : 317 - 328
[8] A new fast asymptotic series for the gamma function
Mortici, Cristinel
[J]. RAMANUJAN JOURNAL, 2015, 38 (03) : 549 - 559
[9] A continued fraction approximation of the gamma function
Mortici, Cristinel
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 402 (02) : 405 - 410
[10] Ramanujan's estimate for the gamma function via monotonicity arguments
Mortici, Cristinel
[J]. RAMANUJAN JOURNAL, 2011, 25 (02) : 149 - 154

← 1 2 →