On formulas and fractional exponents for umbral operators
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917424235806720 |
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| author | Beauduin, Kei |
| author_facet | Beauduin, Kei |
| contents | We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral operators. Third, its proof synthesizes a broad range of existing results in operational calculus and highlights their combined effectiveness. As an illustration, we obtain a new and natural extension of the Laguerre polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On formulas and fractional exponents for umbral operators Beauduin, Kei Combinatorics Classical Analysis and ODEs 05A40, 47B99, 13F25, 39B12, 47B33 We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral operators. Third, its proof synthesizes a broad range of existing results in operational calculus and highlights their combined effectiveness. As an illustration, we obtain a new and natural extension of the Laguerre polynomials. |
| title | On formulas and fractional exponents for umbral operators |
| topic | Combinatorics Classical Analysis and ODEs 05A40, 47B99, 13F25, 39B12, 47B33 |
| url | https://arxiv.org/abs/2512.04638 |