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- W4287691364 abstract "We prove that if $f(x) = sum_{k=0}^infty a_k x^k,$ $a_k >0, $ is an entire function such that the sequence $Q := left( frac{a_k^2}{a_{k-1}a_{k+1}} right)_{k=1}^infty$ is non-decreasing and $frac{a_1^2}{a_{0}a_{2}} geq 2sqrt[3]{2},$ then all but a finite number of zeros of $f$ are real and simple. We also present a criterion in terms of the closest to zero roots for such a function to have only real zeros (in other words, for belonging to the Laguerre--P'olya class of type I) under additional assumption on the sequence $Q.$" @default.
- W4287691364 created "2022-07-26" @default.
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- W4287691364 date "2020-08-08" @default.
- W4287691364 modified "2023-09-24" @default.
- W4287691364 title "On the entire functions from the Laguerre-P'olya I class having the increasing second quotients of Taylor coefficients" @default.
- W4287691364 doi "https://doi.org/10.48550/arxiv.2008.04754" @default.
- W4287691364 hasPublicationYear "2020" @default.
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