On Some Convergence to the Constant and Proof of Keller's Limit

被引：0

作者：

Fang, Siyu ^{[1
]}

Lai, Li ^{[1
]}

Lu, Dawei ^{[1
]}

Wang, Xiaoguang ^{[1
]}

机构：

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

来源：

RESULTS IN MATHEMATICS | 2018年 / 73卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Continued fraction; asymptotic formula; constant e; double inequalities; Keller's limit; INEQUALITIES; APPROXIMATIONS; IMPROVEMENTS;

D O I：

10.1007/s00025-018-0831-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new asymptotic formula for the constant e is proposed by the continued fraction approximation. As a consequence, we deduce inequalities for the sequence (1 + 1/n)(n), and show an application of the inequalities to the proof of Keller's limit. Numerical computations and comparisons are conducted to illustrate the superiority of our new inequalities.

引用

页数：12

共 19 条

[1] [Anonymous], 1972, NBS APPL MATH SERIES
[2] Hu Y., 2006, COMMUN MATH ANAL, V1, P115
[3] Lu DW, 2017, RAMANUJAN J, V43, P69, DOI 10.1007/s11139-015-9765-x
[4] Some new convergent sequences and inequalities of Euler's constant
Lu, Dawei
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 419 (01) : 541 - 552
[5] A new asymptotic expansion and some inequalities for the gamma function
Lu, Dawei
Wang, Xiaoguang
[J]. JOURNAL OF NUMBER THEORY, 2014, 140 : 314 - 323
[6] A generated approximation of the gamma function related to Windschitl's formula
Lu, Dawei
Song, Lixin
Ma, Congxu
[J]. JOURNAL OF NUMBER THEORY, 2014, 140 : 215 - 225
[7] Mortici C, 2015, CARPATHIAN J MATH, V31, P249
[8] On the Ramanujan-Lodge harmonic number expansion
Mortici, Cristinel
Villarino, Mark B.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 251 : 423 - 430
[9] On Ramanujan's large argument formula for the Gamma function
Mortici, Cristinel
[J]. RAMANUJAN JOURNAL, 2011, 26 (02) : 185 - 192
[10] Improved asymptotic formulas for the gamma function
Mortici, Cristinel
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (11) : 3364 - 3369

← 1 2 →