Approximation and inequalities for the factorial function related to the Burnside's formula

被引：0

作者：

You, Xu ^{[1
]}

机构：

[1] Beijing Inst Petrochem Technol, Dept Math & Phys, Beijing 102617, Peoples R China

来源：

CUBO-A MATHEMATICAL JOURNAL | 2024年 / 26卷 / 02期

关键词：

Factorial function; Stirling's formula; Burnside's formula; approximation; continued fraction; MULTIPLE-CORRECTION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a continued fraction approximation and some inequalities of the factorial function based on the Burnside's formula. This approximation is fast in comparison with the recently discovered asymptotic series. Finally, some numerical computations are provided for demonstrating the superiority of our approximation over the Burnside's formula and the classical Stirling's series.

引用

页码：317 / 326

页数：10

共 14 条

[1]

ABRAMOWITZ M, 1972, HDB MATH FUNCTIONS F

[2]

BATIR NECDET, 2008, Proyecciones (Antofagasta), V27, P97

[3]

Burnside W., 1917, Messenger Math, V46, P157

[4] Multiple-correction and continued fraction approximation (II) [J].

Cao, Xiaodong ;

You, Xu .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 261 :192-205

[5] Multiple-correction and continued fraction approximation [J].

Cao, Xiaodong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 424 (02) :1425-1446

[6] Multiple-correction and faster approximation [J].

Cao, Xiaodong ;

Xu, Hongmin ;

You, Xu .

JOURNAL OF NUMBER THEORY, 2015, 149 :327-350

[7] DECISION PROCEDURE FOR INDEFINITE HYPERGEOMETRIC SUMMATION [J].

GOSPER, RW .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1978, 75 (01) :40-42

[8]

Mortici C., 2010, Creat. Math. Inform., V19, P53

[9] Asymptotic Formulas and Inequalities for the Gamma Function in Terms of the Tri-Gamma Function [J].

Mortici, Cristinel ;

Qi, Feng .

RESULTS IN MATHEMATICS, 2015, 67 (3-4) :395-402

[10] Product Approximations via Asymptotic Integration [J].

Mortici, Cristinel .

AMERICAN MATHEMATICAL MONTHLY, 2010, 117 (05) :434-441

← 1 2 →