Leading coefficient in the Hankel determinants related to binomial and $q$-binomial transforms
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914659708174336 |
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| author | Chern, Shane Jiu, Lin Li, Shuhan Wang, Liuquan |
| author_facet | Chern, Shane Jiu, Lin Li, Shuhan Wang, Liuquan |
| contents | It is a standard result that the Hankel determinants for a sequence stay invariant after performing the binomial transform on this sequence. In this work, we extend the scenario to $q$-binomial transforms and study the behavior of the leading coefficient in such Hankel determinants. We also investigate the leading coefficient in the Hankel determinants for even-indexed Bernoulli polynomials with recourse to a curious binomial transform. In particular, the degrees of these Hankel determinants share the same nature as those in one of the $q$-binomial cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Leading coefficient in the Hankel determinants related to binomial and $q$-binomial transforms Chern, Shane Jiu, Lin Li, Shuhan Wang, Liuquan Number Theory Combinatorics Primary 11C20, Secondary 11B68, 33D45 It is a standard result that the Hankel determinants for a sequence stay invariant after performing the binomial transform on this sequence. In this work, we extend the scenario to $q$-binomial transforms and study the behavior of the leading coefficient in such Hankel determinants. We also investigate the leading coefficient in the Hankel determinants for even-indexed Bernoulli polynomials with recourse to a curious binomial transform. In particular, the degrees of these Hankel determinants share the same nature as those in one of the $q$-binomial cases. |
| title | Leading coefficient in the Hankel determinants related to binomial and $q$-binomial transforms |
| topic | Number Theory Combinatorics Primary 11C20, Secondary 11B68, 33D45 |
| url | https://arxiv.org/abs/2401.17220 |