The $q$-Stirling numbers of the second kind and its applications

Kim, Min-Soo ¹ ; Kim, Daeyeoul ²

¹ Division of Mathematics, Science, and Computers, Kyungnam University, 7(Woryeong-dong) kyungnamdaehak-ro, Masanhappo-gu, Changwon-si, Gyeongsangnam-do 51767, Republic of Korea
² Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-si 54896, Republic of Korea

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 8, p. 971-983.

Résumé

The study of $q$-Stirling numbers of the second kind began with Carlitz [L. Carlitz, Duke Math. J., $\textbf{15}$ (1948), 987--1000] in 1948. Following Carlitz, we derive some identities and relations related to $q$-Stirling numbers of the second kind which appear to be either new or else new ways of expressing older ideas more comprehensively.

Détail

DOI : 10.22436/jnsa.011.08.04

Classification : 05A40, 11A25
Keywords: \(q\)-Stirling numbers of the second kind, \(q\)-factorial

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