On the entire functions from the Laguerre-P\'olya I class with non-monotonic second quotients of Taylor coefficients
| Autor: | Nguyen, Thu Hien, Vishnyakova, Anna |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study the entire functions $f(z) = \sum_{k=0}^\infty a_k z^k, a_k>0,$ with non-monotonic second quotients of Taylor coefficients, namely, such that $\frac{a_{2m-1}^2}{a_{2m-2}a_{2m}} = a>1$ and $\frac{a_{2m}^2}{a_{2m-1}a_{2m+1}} = b>1$ for all $m \in \mathbb{N}.$ We obtain necessary and sufficient conditions under which such functions belong to the Laguerre-P\'olya I class. Comment: 20 pages. arXiv admin note: text overlap with arXiv:2008.04754, arXiv:2101.11757 |
| Databáze: | arXiv |
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