Open Access
2018 Infinite series identities involving quadratic and cubic harmonic numbers
Xiaoyuan Wang, Wenchang Chu
Publ. Mat. 62(1): 285-300 (2018). DOI: 10.5565/PUBLMAT6211813


By means of the modified Abel lemma on summation by parts, we investigate infinite series involving quadratic and cubic harmonic numbers. Several infinite series identities are established for $\pi^2$ and $\zeta(3)$ as consequences.


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Xiaoyuan Wang. Wenchang Chu. "Infinite series identities involving quadratic and cubic harmonic numbers." Publ. Mat. 62 (1) 285 - 300, 2018.


Received: 21 November 2016; Revised: 20 April 2017; Published: 2018
First available in Project Euclid: 16 December 2017

zbMATH: 06848695
MathSciNet: MR3738192
Digital Object Identifier: 10.5565/PUBLMAT6211813

Primary: 11M06
Secondary: 40A25

Keywords: Abel's lemma on summation by parts , harmonic numbers , partial fraction decomposition , Riemann zeta function , telescoping method

Rights: Copyright © 2018 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.62 • No. 1 • 2018
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