Some observations on the connection between Stirling numbers and Bessel numbers
Combinatorics
2023-07-06 v1 Classical Analysis and ODEs
Abstract
We present new proofs for some summation identities involving Stirling numbers of both first and second kind. The two main identities show a connection between Stirling numbers and Bessel numbers. Our method is based on solving a particular recurrence relation in two different ways and comparing the coefficients in the resulting polynomial expressions. We also briefly discuss a probabilistic setting where this recurrence relation occurs.
Cite
@article{arxiv.2007.11557,
title = {Some observations on the connection between Stirling numbers and Bessel numbers},
author = {David Stenlund},
journal= {arXiv preprint arXiv:2007.11557},
year = {2023}
}
Comments
10 pages