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

摘要

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