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Research Article | Open Access

The constant in asymptotic expansions for a cubic recurrence

Xiaoyu Luo1,2, Yong-Guo Shi2( ), Kelin Li1, Pingping Zhang3
College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 64300, China
Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China
College of Science, Shandong University of Aeronautics, Binzhou 256603, China
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Abstract

Some properties of the constant in asymptotic expansion of iterates of a cubic function were investigated. This paper analyzed the monotonicity, differentiability of the constant with respect to the initial value and the functional equation that is satisfied.

Keywords

cubic functioniterateasymptotic expansionEuler Maclaurin formula
CLC number: 11B37, 39B12, 41A60

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 21848-21859
DOI: 10.3934/math.20241062

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Cite this article:
Luo X, Shi Y-G, Li K, et al. The constant in asymptotic expansions for a cubic recurrence. AIMS Mathematics, 2024, 9(8): 21848-21859. https://doi.org/10.3934/math.20241062

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Received: 12 May 2024
Revised: 21 June 2024
Accepted: 01 July 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)