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

The study of q-Stirling numbers of the second kind began with Carlitz [L. Carlitz, Duke Math. J., 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.