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arXiv · 2101.01348

Complete and incomplete Bell polynomials associated with Lah-Bell numbers and polynomials

Taekyun Kim·Dae San Kim·Lee-Chae Jang·Hyunseok Lee·Han-Young Kim
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Abstract

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.

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Taekyun Kim, Dae San Kim, Lee-Chae Jang, Hyunseok Lee, Han-Young Kim. 2021-01-05. Complete and incomplete Bell polynomials associated with Lah-Bell numbers and polynomials. https://arxiv.org/abs/2101.01348

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