English

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.

Keywords

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

R2 v1 2026-06-23T17:19:23.512Z