@article{Shi2024, 
author = {Yong-Guo Shi and Xiaoyu Luo and Zhi-jie Jiang},
title = {Asymptotics on a heriditary recursion},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {30443-30453},
keywords = {heriditary recursion, asymptotic expansion, Euler–Maclaurin formula},
url = {https://www.sciopen.com/article/10.3934/math.20241469},
doi = {10.3934/math.20241469},
abstract = {The asymptotic behavior for a heriditary recursion   x1>aandxn+1=1ns∑k=1nf(xkk)for everyn≥1is 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.}
}