Degenerate Euler-Seidel Matrix Method and Their Applications
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911316851032064 |
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| author | Kim, Taekyun Kim, Dae san |
| author_facet | Kim, Taekyun Kim, Dae san |
| contents | This paper introduces a degenerate version of the Euler-Seidel matrix method by incorporating a parameter lambda into the classical recurrence relation. The standard Euler-Seidel method relates the generating functions of an initial sequence and its final sequence via Seidel's formula, Our generalized method establishes transformation formulas using lambda-generalized binomial identities and yields a degenerate Seidel's formula for the exponential generating functions. The results are applied to study and derive new combinatorial identities for sequences like the degenerate Bell and Fubini numbers and polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12542 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degenerate Euler-Seidel Matrix Method and Their Applications Kim, Taekyun Kim, Dae san Number Theory 11B73, 11B83 This paper introduces a degenerate version of the Euler-Seidel matrix method by incorporating a parameter lambda into the classical recurrence relation. The standard Euler-Seidel method relates the generating functions of an initial sequence and its final sequence via Seidel's formula, Our generalized method establishes transformation formulas using lambda-generalized binomial identities and yields a degenerate Seidel's formula for the exponential generating functions. The results are applied to study and derive new combinatorial identities for sequences like the degenerate Bell and Fubini numbers and polynomials. |
| title | Degenerate Euler-Seidel Matrix Method and Their Applications |
| topic | Number Theory 11B73, 11B83 |
| url | https://arxiv.org/abs/2512.12542 |