Kwang-Wu Chen and Yi-Hsuan Chen

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 2, Pages 85–104

DOI: 10.7546/nntdm.2020.26.2.85-104

**Full paper (PDF, 287 Kb)**

## Details

### Authors and affiliations

Kwang-Wu Chen

*Department of Mathematics, University of Taipei
No. 1, Ai-Guo West Road, Taipei 10048, Taiwan
*

Yi-Hsuan Chen

*Department of Mathematics, University of Taipei
No. 1, Ai-Guo West Road, Taipei 10048, Taiwan
*

### Abstract

We use Abel’s summation formula and the method of partial fraction decomposition to study infinite series involving generalized harmonic numbers of any positive integral order, with any positive integral power.

### Keywords

- Abel’s summation formula
- Generalized harmonic functions
- Multiple Hurwitz zeta functions
- Digamma function

### 2010 Mathematics Subject Classification

- 05A19
- 11M06
- 40A25

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## Cite this paper

Chen, K.-W., & Chen, Y.-H. (2020). Infinite series containing generalized harmonic functions. *Notes on Number Theory and Discrete Mathematics*, 26 (2), 85-104, DOI: 10.7546/nntdm.2020.26.2.85-104.