Laala Khaldi, Farid Bencherif and Miloud Mihoubi

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 4, Pages 80–89

DOI: 10.7546/nntdm.2021.27.4.80-89

**Full paper (PDF, 207 Kb)**

## Details

### Authors and affiliations

Laala Khaldi

*Department of Mathematics, University of Bouira,
10000 Bouira, Algeria
*

*Laboratory EDPNL&HM, Department of Mathematics,*

ENS, BP 92, Vieux-Kouba, Algeria

ENS, BP 92, Vieux-Kouba, Algeria

Farid Bencherif

*Laboratory LA3C, Faculty of Mathematics, USTHB
BP 32, El Alia , 16111, Algiers, Algeria
*

Miloud Mihoubi

*Laboratory RECITS, Faculty of Mathematics, USTHB
BP 32, El Alia, 16111, Algiers, Algeria
*

### Abstract

In this paper, we give several explicit formulas involving the -th Euler polynomial For any fixed integer , the obtained formulas follow by proving that can be written as a linear combination of the polynomials , with . As consequence, some explicit formulas for Bernoulli numbers may be deduced.

### Keywords

- Appell polynomials
- Euler polynomials
- Bernoulli numbers
- Binomial coefficients

### 2020 Mathematics Subject Classification

- 11B68
- 05A10

### References

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## Cite this paper

Khaldi, L., Bencherif, F., & Mihoubi, M. (2021). Explicit formulas for Euler polynomials and Bernoulli numbers. *Notes on Number Theory and Discrete Mathematics*, 27(4), 80-89, DOI: 10.7546/nntdm.2021.27.4.80-89.