Summation formulae in relation to Euler sums

被引：6

作者：

Yang, Jizhen ^{[1
]}

Wang, Yunpeng ^{[2
]}

机构：

[1] Luoyang Normal Coll, Dept Math, Luoyang, Peoples R China

[2] Luoyang Inst Sci & Technol, Dept Math & Phys, Luoyang, Peoples R China

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2017年 / 28卷 / 05期

关键词：

Summation formulae; Riemann zeta functions; harmonic numbers; Q-HARMONIC NUMBERS; MATHEMATICAL CONSTANTS; SERIES REPRESENTATIONS; BINOMIAL COEFFICIENTS; IDENTITIES;

D O I：

10.1080/10652469.2017.1293669

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate some formulae related to Euler Sums and give the closed-form representations for the sum Sigma(n >= 1) H-n/(n+m m)(n+k k) which can be evaluated in terms of the Riemann zeta functions and generalized harmonic numbers.

引用

页码：336 / 349

页数：14

共 14 条

[1] Some new formulas for π [J].

Almkvist, G ;

Krattenthaler, C ;

Petersson, J .

EXPERIMENTAL MATHEMATICS, 2003, 12 (04) :441-456

[2] Series representations for γ and other mathematical constants [J].

Alzer, Horst ;

Koumandos, Stamatis .

ANALYSIS MATHEMATICA, 2008, 34 (01) :1-8

[3] 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

[4]

[Anonymous], COMPUTATIONAL TECHNI

[5]

Comtet L., 1974, Advanced combinatorics

[6] Automatic generation of hypergeometric identities by the beta integral method [J].

Krattenthaler, C ;

Rao, KS .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 160 (1-2) :159-173

[7] EXTENSIONS OF EULER HARMONIC SUMS [J].

Sofo, Anthony ;

Cvijovic, Djurdje .

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2012, 6 (02) :317-328

[8]

Sofo A, 2011, ANAL MATH, V37, P51, DOI 10.1007/s10476-011-0103-2

[9] Integral forms of sums associated with harmonic numbers [J].

Sofo, Anthony .

APPLIED MATHEMATICS AND COMPUTATION, 2009, 207 (02) :365-372

[10] SOME MORE IDENTITIES INVOLVING RATIONAL SUMS [J].

Sofo, Anthony .

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2008, 2 (01) :56-64

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