This paper proposes a method that identifies integer N for $P$-recursive sequences, suggesting connections to turán and laguerre inequalities.
The Turán 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 \√[n]aₙ/n! ≥ N and \√[n+1]aₙ₊₁/(√[n]aₙ n!) ≥ N satisfy the higher order Turán inequality and the Laguerre inequality of order two for a P-recursive sequence ₙ ≥ 1.
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Zhongjie Li (2025) studied this question.
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