Recurrence relations for harmonic and derangement numbers
Number Theory
2025-09-15 v1
Abstract
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the underlying structure of these numbers but also highlight the effectiveness of elementary techniques in discovering new mathematical properties. The findings have potential applications in various fields where these numbers appear, including combinatorics, probability, and computer science.
Cite
@article{arxiv.2509.10404,
title = {Recurrence relations for harmonic and derangement numbers},
author = {Taekyun Kim and Dae san Kim and Jongkyum Kwon and Kyo-Shin Hwang},
journal= {arXiv preprint arXiv:2509.10404},
year = {2025}
}
Comments
7 pages