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Research Article | Open Access

Asymptotics on a heriditary recursion

Yong-Guo Shi1, Xiaoyu Luo2( ), Zhi-jie Jiang2
Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China
College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 64300, China
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Abstract

The asymptotic behavior for a heriditary recursion

x1>aandxn+1=1ns∑k=1nf(xkk)for everyn≥1

is studied, where f is decreasing, continuous on (a,∞) ( a<0), and twice differentiable at 0. The result has been known for the case s=1. This paper analyzes the case s>1. We obtain an asymptotic sequence that is quite different from the case s=1. Some examples and applications are provided.

Keywords

heriditary recursionasymptotic expansionEuler–Maclaurin formula
CLC number: 03D99, 11B37, 41A60, 65B15

References

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 30443-30453
DOI: 10.3934/math.20241469

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Cite this article:
Shi Y-G, Luo X, Jiang Z-j. Asymptotics on a heriditary recursion. AIMS Mathematics, 2024, 9(11): 30443-30453. https://doi.org/10.3934/math.20241469

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Received: 21 July 2024
Revised: 10 October 2024
Accepted: 16 October 2024
Published: 25 October 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)