On a q-analogue for Bernoulli numbers

Inspired by Borwein et al. (Am. Math. Mon., 116(5):387-412, 2009), we define a sequence of q-analogues for the Bernoulli numbers under the framework of Strodt operators. We show that they not only satisfy identities similar to those of the q-analogue proposed by Carlitz (Duke Math. J., 15(4):987-1000, 1948), but also interesting analytical properties as functions of q. In particular, we give a simple analytic proof of a generalization of an explicit formula for the Bernoulli numbers given by Woon (Math. Mag., 70(1):51-56, 1997). We also define a set of q-analogues for the Stirling numbers of the second kind within our framework and prove a q-extension of a related, well-known closed form relating Bernoulli and Stirling numbers.