A note on degenerate derangement polynomials and numbers

AIMS Mathematics

Hyunseok Lee¹  Taekyun Kim¹  Dae San Kim²  Lee-Chae Jang³ 

[1] 1. Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea;2. Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea;3. Graduate School of Education, Konkuk University, Seoul 143-701, Republic of Korea;

关键词: degenerate derangement polynomials;    degenerate gamma distribution;    degenerate fubini polynomials;    fully degenerate bell polynomials;    degenerate stirling numbers;   

DOI  :  10.3934/math.2021380

来源: DOAJ

【 摘 要 】

In this paper, we study the degenerate derangement polynomials and numbers, investigate some properties of those polynomials and numbers and explore their connections with the degenerate gamma distributions. In more detail, we derive their explicit expressions, recurrence relations and some identities involving the degenerate derangement polynomials and numbers and other special polynomials and numbers, which include the fully degenerate Bell polynomials, the degenerate Fubini polynomials and the degenerate Stirling numbers of both kinds. We also show that those polynomials and numbers are connected with the moments of some variants of the degenerate gamma distributions.

【 授权许可】

Unknown