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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.16348 |
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| _version_ | 1866912746986012672 |
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| author | Beauduin, Kei |
| author_facet | Beauduin, Kei |
| contents | In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to umbral operators. We also give an in-depth study of the generating functions associated to umbral calculus, and show how these lead to short proofs of several advanced results, including the Lagrange-Bürmann inversion theorem. Finally, we discuss pseudoinverses for delta operators and illustrate our methods with a variety of examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operational Umbral Calculus Beauduin, Kei Combinatorics Number Theory 05A40, 13F25, 11B73, 05A10, 05A19, 47B99, 11B68, 11B37 In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to umbral operators. We also give an in-depth study of the generating functions associated to umbral calculus, and show how these lead to short proofs of several advanced results, including the Lagrange-Bürmann inversion theorem. Finally, we discuss pseudoinverses for delta operators and illustrate our methods with a variety of examples. |
| title | Operational Umbral Calculus |
| topic | Combinatorics Number Theory 05A40, 13F25, 11B73, 05A10, 05A19, 47B99, 11B68, 11B37 |
| url | https://arxiv.org/abs/2407.16348 |