Necdet Batır and Anthony Sofo

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 29, 2023, Number 1, Pages 78–97

DOI: 10.7546/nntdm.2023.29.1.78-97

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## Details

### Authors and affiliations

Necdet Batır

*Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Turkey*

Anthony Sofo

*College of Engineering and Science, Victoria University, Australia*

### Abstract

We offer a number of various finite and infinite sum identities involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers. For example, among many others, we prove

and

where are Bernoulli numbers of the second kind, and is the Riemann zeta function. We also give an alternate proof of the series representations for the constants and given by Blagouchine and Coppo.

### Keywords

- Binomial sums
- Harmonic sums
- Binomial coefficients
- Gregory coefficients
- Bernoulli numbers of the second kind
- Polygamma functions
- Riemann zeta function
- Harmonic numbers

### 2020 Mathematics Subject Classification

- 05A10
- 05A19

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### Manuscript history

- Received: 30 June 2022
- Revised: 9 January 2023
- Accepted: 23 February 2023
- Online First: 27 February 2023

### Copyright information

Ⓒ 2023 by the Authors.

This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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## Cite this paper

Batır, N., & Sofo, A. (2023). Sums involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers. *Notes on Number Theory and Discrete Mathematics*, 29(1), 78-97, DOI: 10.7546/nntdm.2023.29.1.78-97.