The \(q\)-Stirling numbers of the second kind and its applications

Volume 11, Issue 8, pp 971--983
Publication Date: June 09, 2018 Submission Date: March 31, 2018 Revision Date: May 01, 2018 Accteptance Date: May 03, 2018


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


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.