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arXiv · 2412.18304

Inequalities associated with the root sequences of P-recursive sequences

Zhongjie Li
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Abstract

The Tur{á}n inequalities and the Laguerre inequalities are closely related to the Laguerre-Pólya class and the Riemann hypothesis. These inequalities have been extensively studied in the literature. In this paper, we propose a method to determine a positive integer $N$ such that the sequences $\{\sqrt[n]{a_n}/n!\}_{n \ge N}$ and $\{\sqrt[n+1]{a_{n+1}}/(\sqrt[n]{a_n} n!)\}_{n \ge N}$ satisfy the higher order Tur{á}n inequalities and the Laguerre inequalities of order two for a P-recursive sequence $\{a_n\}_{n \ge 1}$.

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Zhongjie Li. 2024-12-24. Inequalities associated with the root sequences of P-recursive sequences. https://arxiv.org/abs/2412.18304

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