### AIMS Mathematics

2022, Issue 9: 17357-17368. doi: 10.3934/math.2022956
Research article

# Some identities involving degenerate Stirling numbers arising from normal ordering

• Received: 25 April 2022 Revised: 04 July 2022 Accepted: 14 July 2022 Published: 26 July 2022
• MSC : 11B73, 11B83

• In this paper, we derive some identities and recurrence relations for the degenerate Stirling numbers of the first kind and of the second kind, which are degenerate versions of the ordinary Stirling numbers of the first kind and of the second kind. They are deduced from the normal orderings of degenerate integral powers of the number operator and their inversions, certain relations of boson operators and the recurrence relations of the Stirling numbers themselves. Here we note that, while the normal ordering of an integral power of the number operator is expressed with the help of the Stirling numbers of the second kind, that of a degenerate integral power of the number operator is represented by means of the degenerate Stirling numbers of the second kind.

Citation: Taekyun Kim, Dae San Kim, Hye Kyung Kim. Some identities involving degenerate Stirling numbers arising from normal ordering[J]. AIMS Mathematics, 2022, 7(9): 17357-17368. doi: 10.3934/math.2022956

### Related Papers:

• In this paper, we derive some identities and recurrence relations for the degenerate Stirling numbers of the first kind and of the second kind, which are degenerate versions of the ordinary Stirling numbers of the first kind and of the second kind. They are deduced from the normal orderings of degenerate integral powers of the number operator and their inversions, certain relations of boson operators and the recurrence relations of the Stirling numbers themselves. Here we note that, while the normal ordering of an integral power of the number operator is expressed with the help of the Stirling numbers of the second kind, that of a degenerate integral power of the number operator is represented by means of the degenerate Stirling numbers of the second kind.

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