Quadratic alternating harmonic number sums

被引：53
作者：
Sofo, Anthony [1 ]
机构：
[1] Victoria Univ, Melbourne, Vic 8001, Australia
来源：
JOURNAL OF NUMBER THEORY | 2015年 / 154卷
关键词：
Combinatorial series identities; Summation formulas; Partial fraction approach; Alternating harmonic numbers; Binomial coefficients; Polylogarithm function; IDENTITIES; DIGAMMA;
D O I：
10.1016/j.jnt.2015.02.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop new closed form representations of sums of quadratic alternating harmonic numbers and reciprocal binomial coefficients. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：144 / 159
页数：16
相关论文
共 26 条
[1]  
[Anonymous], COMPUTATIONAL TECHNI
[2]  
[Anonymous], 2012, Zeta and q-zeta functions and associated series and integrals
[3]   The evaluation of character Euler double sums [J].
Borwein, J. M. ;
Zucker, I. J. ;
Boersma, J. .
RAMANUJAN JOURNAL, 2008, 15 (03) :377-405
[4]   Values of the polygamma functions at rational arguments (vol 40, pg 15019, 2007) [J].
Choi, J. ;
Cvijovic, D. .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (23)
[5]  
Choi J., 2013, J INEQUAL APPL, V49
[6]   Some summation formulas involving harmonic numbers and generalized harmonic numbers [J].
Choi, Junesang ;
Srivastava, H. M. .
MATHEMATICAL AND COMPUTER MODELLING, 2011, 54 (9-10) :2220-2234
[7]   On generalized harmonic number sums [J].
Coffey, Mark W. ;
Lubbers, Nicholas .
APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (02) :689-698
[8]   On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams [J].
Coffey, MW .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 183 (01) :84-100
[9]   A note on harmonic numbers, umbral calculus and generating functions [J].
Dattoli, G. ;
Srivastava, H. M. .
APPLIED MATHEMATICS LETTERS, 2008, 21 (07) :686-693
[10]   Euler sums and contour integral representations [J].
Flajolet, P ;
Salvy, B .
EXPERIMENTAL MATHEMATICS, 1998, 7 (01) :15-35
123