Degenerate Algorithms for degenerate Bernoulli and Euler numbers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915703816192000 |
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| author | Kim, Taekyun Kim, Dae san |
| author_facet | Kim, Taekyun Kim, Dae san |
| contents | This paper introduces and investigates degenerate versions of the A-algorithm and B-algorithm by incorporating a parameter lambda into their respective recurrence relations. We derive explicit formulas for the final sequences of these algorithms in terms of the initial sequences and the degenerate Stirling numbers of the second kind. Furthermore, we establish functional relationships between the ordinary generating functions of the initial sequences and the exponential generating functions of the final sequences. Specifically, we demonstrate that these degenerate algorithms yield degenerate Bernoulli and Euler numbers under specific initial conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00356 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Degenerate Algorithms for degenerate Bernoulli and Euler numbers Kim, Taekyun Kim, Dae san Number Theory 11B68, 11B73 This paper introduces and investigates degenerate versions of the A-algorithm and B-algorithm by incorporating a parameter lambda into their respective recurrence relations. We derive explicit formulas for the final sequences of these algorithms in terms of the initial sequences and the degenerate Stirling numbers of the second kind. Furthermore, we establish functional relationships between the ordinary generating functions of the initial sequences and the exponential generating functions of the final sequences. Specifically, we demonstrate that these degenerate algorithms yield degenerate Bernoulli and Euler numbers under specific initial conditions. |
| title | Degenerate Algorithms for degenerate Bernoulli and Euler numbers |
| topic | Number Theory 11B68, 11B73 |
| url | https://arxiv.org/abs/2601.00356 |