Hye Kyung Kim

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 28, 2022, Number 4, Pages 666–676

DOI: 10.7546/nntdm.2022.28.4.666-676

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## Details

### Authors and affiliations

Hye Kyung Kim

*Department of Mathematics Education, Daegu Catholic University
Gyeongsan 38430, Republic of Korea*

### Abstract

In this paper, we introduce a new type degenerate Stirling numbers of the second kind and their degenerate Bell polynomials, which is different from degenerate Stirling numbers of the second kind studied so far. We investigate the explicit formula, recurrence relation and Dobinski-like formula of a new type degenerate Stirling numbers of the second kind. We also derived several interesting expressions and identities for bell polynomials of these new type degenerate Stirling numbers of the second kind including the generating function, recurrence relation, differential equation with Bernoulli number as coefficients, the derivative and Riemann integral, so on.

### Keywords

- Stirling numbers of the first and second kind
- Degenerate Stirling numbers of the second kind
- Bell polynomials
- Bernoulli polynomials

### 2020 Mathematics Subject Classification

- 05A15
- 05A18
- 11B68

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### Manuscript history

- Received: 19 July 2022
- Revised: 22 September 2022
- Accepted: 24 October 2022
- Online First: 27 October 2022

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## Cite this paper

Kim, H. K. (2022). New type degenerate Stirling numbers and Bell polynomials. *Notes on Number Theory and Discrete Mathematics*, 28(4), 666-676, DOI: 10.7546/nntdm.2022.28.4.666-676.