A New Expression for the Bernoulli Numbers and its Applications
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912872199618560 |
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| author | Kargın, Levent Mutluer, Merve |
| author_facet | Kargın, Levent Mutluer, Merve |
| contents | This paper shows that a finite discrete convolution involving Stirling numbers of both kinds and harmonic numbers can be expressed in terms of the Bernoulli numbers. As applications of this expression, the linear recurrence relation for the Bernoulli numbers given by Agoh is reproved, and a new recurrence relation for the Bernoulli numbers is obtained. Furthermore, it is shown that a cumulative sum of the Bernoulli numbers can be written in terms of the Bernoulli and di-Bernoulli numbers. Finally, congruences for the sums of the Bernoulli and Euler numbers are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03440 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A New Expression for the Bernoulli Numbers and its Applications Kargın, Levent Mutluer, Merve Number Theory Combinatorics 11A07, 11B68, 11B73 This paper shows that a finite discrete convolution involving Stirling numbers of both kinds and harmonic numbers can be expressed in terms of the Bernoulli numbers. As applications of this expression, the linear recurrence relation for the Bernoulli numbers given by Agoh is reproved, and a new recurrence relation for the Bernoulli numbers is obtained. Furthermore, it is shown that a cumulative sum of the Bernoulli numbers can be written in terms of the Bernoulli and di-Bernoulli numbers. Finally, congruences for the sums of the Bernoulli and Euler numbers are established. |
| title | A New Expression for the Bernoulli Numbers and its Applications |
| topic | Number Theory Combinatorics 11A07, 11B68, 11B73 |
| url | https://arxiv.org/abs/2602.03440 |