Sumit Kumar Jha

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 2, Pages 148–151

DOI: 10.7546/nntdm.2020.26.2.148-151

**Full paper (PDF, 129 Kb)**

## Details

### Authors and affiliations

Sumit Kumar Jha

*International Institute of Information Technology
Hyderabad-500 032, India
*

### Abstract

Let denote the Bernoulli numbers, and denote the Stirling numbers of the second kind. We prove the following explicit formula

To the best of our knowledge, the formula is new.

### Keywords

- Bernoulli numbers
- Stirling numbers of the second kind
- Riemann zeta function
- Polylogarithm function

### 2010 Mathematics Subject Classification

- 11B68

### References

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## Cite this paper

Jha, S. K. (2020). A new explicit formula for the Bernoulli numbers in terms of the Stirling numbers of the second kind. *Notes on Number Theory and Discrete Mathematics*, 26 (2), 148-151, DOI: 10.7546/nntdm.2020.26.2.148-151.