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

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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

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10.37236/9843

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

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

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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.",

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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.

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DO - 10.37236/9843

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AN - SCOPUS:85125367876

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On the connection between Stirling numbers and Bessel numbers

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