Inequalities associated with the root sequences of P-recursive sequences

Abstract: The Tur{\'a}n inequalities and the Laguerre inequalities are closely related to the Laguerre-P\'{o}lya 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{\'a}n inequalities and the Laguerre inequalities of order two for a P-recursive sequence ${a_n}{n \ge 1}$.