New type degenerate Stirling numbers and Bell polynomials

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
Full paper (PDF, 185 Kb)

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