On the connection between Stirling numbers and Bessel numbers

David Stenlund

doi:10.37236/9843

On the connection between Stirling numbers and Bessel numbers

David Stenlund^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

2 Citations (Scopus)

35 Downloads (Pure)

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.

Original language	English
Article number	P1.40
Journal	Electronic Journal of Combinatorics
Volume	29
Issue number	1
DOIs	https://doi.org/10.37236/9843
Publication status	Published - 2022
MoE publication type	A1 Journal article-refereed

Funding

∗Supported by a grant from the Magnus Ehrnrooth Foundation.

Access to Document

10.37236/9843

On the connection betweenFinal published version, 285 KBLicence: CC BY

https://urn.fi/URN:NBN:fi-fe2023022228216

Cite this

@article{49b8564680834bf4a5921995f92bd3c9,

title = "On the connection between Stirling numbers and Bessel numbers",

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.",

author = "David Stenlund",

note = "Funding Information: ∗Supported by a grant from the Magnus Ehrnrooth Foundation. Publisher Copyright: {\textcopyright} The author.",

year = "2022",

doi = "10.37236/9843",

language = "English",

volume = "29",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Electronic Journal of Combinatorics",

number = "1",

}

TY - JOUR

T1 - On the connection between Stirling numbers and Bessel numbers

AU - Stenlund, David

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85125367876

U2 - 10.37236/9843

DO - 10.37236/9843

M3 - Article

AN - SCOPUS:85125367876

SN - 1077-8926

VL - 29

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 1

M1 - P1.40

ER -

On the connection between Stirling numbers and Bessel numbers

Abstract

Funding

Access to Document

Other files and links

Fingerprint

Cite this