Details

Autor(en) / Beteiligte

• Kim, Dae San
• Kim, Hye Kyung
• Kim, Taekyun

Titel

New approach to $ \lambda $-Stirling numbers

Ist Teil von

• AIMS mathematics, 2023-01, Vol.8 (12), p.28322-28333

Ort / Verlag

AIMS Press

Erscheinungsjahr

2023

Link zum Volltext

Quelle

Elektronische Zeitschriftenbibliothek (Open access)

Beschreibungen/Notizen

• The aim of this paper is to study the $ \lambda $-Stirling numbers of both kinds, which are $ \lambda $-analogues of Stirling numbers of both kinds. These numbers have nice combinatorial interpretations when $ \lambda $ are positive integers. If $ \lambda = 1 $, then the $ \lambda $-Stirling numbers of both kinds reduce to the Stirling numbers of both kinds. We derive new types of generating functions of the $ \lambda $-Stirling numbers of both kinds which are related to the reciprocals of the generalized rising factorials. Furthermore, some related identities are also derived from those generating functions. In addition, all the corresponding results to the $ \lambda $-Stirling numbers of both kinds are obtained for the $ \lambda $-analogues of $ r $-Stirling numbers of both kinds, which are generalizations of those numbers.