The constant in asymptotic expansions for a cubic recurrence

Xiaoyu Luo; Yong-Guo Shi; Kelin Li; Pingping Zhang; Xiaoyu Luo; Yong-Guo Shi; Kelin Li; Pingping Zhang

doi:10.3934/math.20241062

AIMS Mathematics

2024, Volume 9, Issue 8: 21848-21859. doi: 10.3934/math.20241062

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The constant in asymptotic expansions for a cubic recurrence

1.
College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 64300, China
2.
Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China
3.
College of Science, Shandong University of Aeronautics, Binzhou 256603, China

Received: 12 May 2024 Revised: 21 June 2024 Accepted: 01 July 2024 Published: 10 July 2024
MSC : 11B37, 39B12, 41A60

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.
- cubic function,
- iterate,
- asymptotic expansion,
- Euler Maclaurin formula
Citation: Xiaoyu Luo, Yong-Guo Shi, Kelin Li, Pingping Zhang. The constant in asymptotic expansions for a cubic recurrence[J]. AIMS Mathematics, 2024, 9(8): 21848-21859. doi: 10.3934/math.20241062

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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.

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