On the entire functions from the Laguerre-P\'olya I class with non-monotonic second quotients of Taylor coefficients

Thu Hien Nguyen; Anna Vishnyakova

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arXiv · 2107.13061

On the entire functions from the Laguerre-P\'olya I class with non-monotonic second quotients of Taylor coefficients

Thu Hien Nguyen·Anna Vishnyakova

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Abstract

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.

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Thu Hien Nguyen, Anna Vishnyakova. 2021-07-27. On the entire functions from the Laguerre-P\'olya I class with non-monotonic second quotients of Taylor coefficients. https://arxiv.org/abs/2107.13061

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