q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients

A purpose of this paper is to present a systemic study of some families of multiple q-Bernoulli numbers and polynomials by using the multivariate q-Volkenborn integral (= p-adic q-integral) on ℤ p . Moreover, the study of these higher-order q-Bernoulli numbers and polynomials implies some interesting q-analogs of Stirling number identities.