Complete and incomplete Bell polynomials associated with Lah-Bell numbers and polynomials
Kim, Taekyun, Kim, Dae San, Jang, Lee-Chae, Lee, Hyunseok, Kim, Han-Young
ADVANCES IN DIFFERENCE EQUATIONS, 2021, Vol.2021 No.1
- 주제(키워드) 도움말 Incomplete r-extended Lah-Bell polynomial , Complete r-extended Lah-Bell polynomial , 11B73 , 11B83 , 05A19
- 발행기관 SPRINGER
- 발행년도 2021
- 총서유형 Journal
- 본문언어 영어
- 초록/요약 도움말moremore
- The nth r-extended Lah-Bell number is defined as the number of ways a set with n+r elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to introduce incomplete r-extended Lah-Bell polynomials and complete r-extended Lah-Bell polynomials respectively as multivariate versions of r-Lah numbers and the r-extended Lah-Bell numbers and to investigate some properties and identities for these polynomials. From these investigations we obtain some expressions for the r-Lah numbers and the r-extended Lah-Bell numbers as finite sums.
- The nth r-extended Lah-Bell number is defined as the number of ways a set with n+r elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to introduce incomplete r-extended Lah-Bell polynomials and complete r-extended Lah-Bell polynomials respectively as multivariate versions of r-Lah numbers and the r-extended Lah-Bell numbers and to investigate some properties and identities for these polynomials. From these investigations we obtain some expressions for the r-Lah numbers and the r-extended Lah-Bell numbers as finite sums.
