Optimal rate of convergence for sequences of a prescribed form

被引：10

作者：

Gavrea, Ioan ^{[1
]}

Ivan, Mircea ^{[1
]}

机构：

[1] Tech Univ Cluj Napoca, Dept Math, Str Memorandumului 28, Cluj Napoca 400114, Romania

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 402卷 / 01期

关键词：

Euler-Maclaurin formula; Asymptotic expansions; Euler-Mascheroni constant; PARTIAL-SUMS; EULER; LANDAU; CONSTANTS; INEQUALITIES; SERIES;

D O I：

10.1016/j.jmaa.2012.12.070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a highly convergent version of the generalized Euler sequence and we determine the element with the optimal rate of convergence in several classes of sequences of a prescribed form. The new approach extends and unifies many previous efforts in this direction. In addition, we answer an open problem on the asymptotic expansion of the Harmonic number sequence. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：35 / 43

页数：9

共 42 条

[1] Inequalities for the constants of Landau and Lebesgue [J].

Alzer, H .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 139 (02) :215-230

[2] Series representations for some mathematical constants [J].

Alzer, Horst ;

Karayannakis, Dimitri ;

Srivastava, H. M. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 320 (01) :145-162

[3]

[Anonymous], 2000, MATH SLOVACA

[4] An elementary view of Euler's summation formula [J].

Apostol, TM .

AMERICAN MATHEMATICAL MONTHLY, 1999, 106 (05) :409-418

[5] PARTIAL SUMS OF INFINITE SERIES, AND HOW THEY GROW [J].

BOAS, RP .

AMERICAN MATHEMATICAL MONTHLY, 1977, 84 (04) :237-258

[6]

BOAS RP, 1977, MATH COMPUT, V31, P257, DOI 10.1090/S0025-5718-1977-0440862-0

[7]

CHEN CHAO-PING, 2010, [Proceedings of the Jangjeon Mathematical Society, Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)], V13, P299

[8]

Chen CP, 2011, BULL MATH ANAL APPL, V3, P134

[9] New sequence converging towards the Euler-Mascheroni constant [J].

Chen, Chao-Ping ;

Mortici, Cristinel .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (04) :391-398

[10] Approximation formulas for Landau's constants [J].

Chen, Chao-Ping .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 387 (02) :916-919

← 1 2 3 4 5 →