Rational reductions for holonomic sequences
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909085326114816 |
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| author | Wang, Rong-Hua |
| author_facet | Wang, Rong-Hua |
| contents | Given a holonomic sequence $F(n)$, we characterize rational functions $r(n)$ so that $r(n)F(n)$ can be summable. We provide upper and lower bounds on the degree of the numerator of $r(k)$ and show the denominator of $r(n)$ can be read from annihilators of $F(k)$. This illustration provides the so-called rational reductions which can be used to generate new multi-sum equalities and congruences from known ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational reductions for holonomic sequences Wang, Rong-Hua Combinatorics Given a holonomic sequence $F(n)$, we characterize rational functions $r(n)$ so that $r(n)F(n)$ can be summable. We provide upper and lower bounds on the degree of the numerator of $r(k)$ and show the denominator of $r(n)$ can be read from annihilators of $F(k)$. This illustration provides the so-called rational reductions which can be used to generate new multi-sum equalities and congruences from known ones. |
| title | Rational reductions for holonomic sequences |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.15887 |