Finite sums in higher order powers of shifted-harmonic numbers

doi:10.3969/j.issn.1000-5641.2021.06.003

Abstract

CLC Number:

O157

Qinglun YAN, Zhaofen WANG, Juan MI. Finite sums in higher order powers of shifted-harmonic numbers[J]. Journal of East China Normal University(Natural Science), 2021, 2021(6): 24-32.

References 10

1	SRIVASTAVA H M, CHOI J. Zeta and q-Zeta Functions and Associated Series and Integrals [M]. Amsterdam: Elsevier Science Publishers, 2012.
2	SOFO A. Quadratic alternating harmonic number sums. Journal of Number Theory, 2015, 154, 144- 159. doi: 10.1016/j.jnt.2015.02.013
3	SOFO A. Harmonic sums and integral representations. Journal of Applied Analysis, 2010, 16, 265- 277.
4	WEIDEMAN J A C. Pade approximations to the logarithm I: Derivation via differential equations. Quaestiones Mathematicae, 2005, 28 (3): 375- 390. doi: 10.2989/16073600509486135
5	DRIVER K, PRODINGER H, SCHNEIDER C, et al. Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation. Ramanujan Journal, 2006, 11 (2): 139- 158. doi: 10.1007/s11139-006-6503-4
6	SOFO A. Identities for alternating inverse squared binomial and harmonic number sums. Mediterranean Journal of Mathematics, 2016, 13 (4): 1407- 1418. doi: 10.1007/s00009-015-0574-7
7	SOFO A. Finite sums in higher order powers of harmonic numbers. Bull Math Anal Appl, 2013, (5): 71- 79.
8	XU C. Explicit evaluation of harmonic sums. Communications of the Korean Mathematical Society, 2017, 33 (1): 13- 36.
9	SOFO A, SRIVASTAVA H M. A family of shifted harmonic sums. Ramanujan Journal, 2015, 37 (1): 89- 108. doi: 10.1007/s11139-014-9600-9
10	SOFO A. Shifted harmonic sums of order two. Communications of the Korean Mathematical Society, 2014, 29 (2): 239- 255. doi: 10.4134/CKMS.2014.29.2.239

[1]	XU Jian-zhong, MO Jia-qi. Perturbation solution for a solitary wave of the nonlinear higher dimensional disturbed Klein-Gordon equation [J]. Journal of East China Normal University(Natural Sc, 2019, 2019(6): 21-28.
[2]	HAN Xin-yin, YAO Min, ZUO Lian-cui, ZHOU Wei-na. (d,1)-total labeling of lexicographic products of some classes of graphs [J]. Journal of East China Normal University(Natural Sc, 2019, 2019(3): 35-41.
[3]	CHEN Ting, WANG Chen-ying. A q-analogy of a nonterminating ₇F₆-series summation [J]. Journal of East China Normal University(Natural Sc, 2019, 2019(3): 55-62.
[4]	ZHANG Yi, LIU Zhi-qiang, ZOU Si-si, WEN Li-min. Estimation of loss reserves based on a hierarchical bayesian model [J]. Journal of East China Normal University(Natural Sc, 2019, 2019(1): 13-23.
[5]	CHEN Xiao-feng, WANG Yi-qiao. L(2, 1)-labelling of Halin graphs with a maximum degree of seven [J]. Journal of East China Normal University(Natural Sc, 2019, 2019(1): 39-47,57.
[6]	SHI Xue-qin, TANG Xia, WEI Yu-mei, WANG Jian. Study and investigation of Lejeuneaceae species diversity in Anhui Province [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(4): 138-146.
[7]	ZHANG Quan-rui, LIU Jian-cheng. L² harmonic 2-forms on a hypersurface in Euclidean space [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(3): 38-45.
[8]	SU Ya-pan, PAN Hai-lin, ZHAO Zhen-jie, YUAN Meng-ping. Influence of dipolar magnetic interaction on the LDGMI effect of Fe-based nanocrystalline ribbons [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(3): 129-135,156.
[9]	SUN Hui, YAO Bing. Exploring equivalent definitions of eulerian graphs [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(2): 23-30,40.
[10]	CHEN Shao-jun, LI Xiao-tao, ZHENG Jun-hua. Research progress of the target proteins by proteasome activator REGγ in human cancers [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(2): 125-130,159.
[11]	ZHOU Xiao-xiao, BI Chun-juan, WANG Meng, ZHOU Ya, CHEN Zhen-lou. Pollution effects of atmospheric deposition on heavy metals in leafy vegetables and its health risks [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(2): 141-150.
[12]	GUAN Chong-hu, CHEN Jing. A free boundary problem in variational inequality with gradient constraint [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(1): 1-10.
[13]	LI Yi-chun, SUN Hui, YAO Bing. Edge-magic even-gracefulness of several kinds of spread network models [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(1): 11-16,23.
[14]	DONG Yong-peng, WANG Qian-ru, MA Jiao-jiao. A stability theorem for solutions of general time interval multidimensional BSDEs with uniformly continuous generators [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(1): 24-34,49.
[15]	YANG Yan-yan, WEI Wen-long, HUANG Zhi-gang. Meromorphic solutions of some type of system of differential and difference equations [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(1): 50-58.

Finite sums in higher order powers of shifted-harmonic numbers

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References 10

Related Articles 15

Recommended Articles

Metrics

Comments