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

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Finite sums in higher order powers of shifted-harmonic numbers

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