Geodesic
Inequalities associated with the root sequences of \(P\)-recursive sequences
Zhongjie Li1
1TIanjin University
The electronic journal of combinatorics, Tome 32 (2025) no. 4
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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 $\{\sqrt[n]{a_n}/n!\}_{n \ge N}$ and $\{\sqrt[n+1]{a_{n+1}}/(\sqrt[n]{a_n} n!)\}_{n \ge N}$ satisfy the higher order Turán inequality and the Laguerre inequality of order two for a $P$-recursive sequence $\{a_n\}_{n \ge 1}$.
DOI : 10.37236/13524
Classification : 05A20, 41A60
Mots-clés : Turán inequality, Laguerre inequality

Zhongjie Li  1

1 TIanjin University 
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     author = {Zhongjie Li},
     title = {Inequalities associated with the root sequences of {\(P\)-recursive} sequences},
     journal = {The electronic journal of combinatorics},
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Zhongjie Li. Inequalities associated with the root sequences of \(P\)-recursive sequences. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13524

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