Sums of Products of Twoq-Bernoulli Numbers Original Research Article

We extend a well-known formula for sums of products of two Bernoulli numbers to that of Carlitzʹsq-Bernoulli numbers. Recently Dilcher (J. Number Theory60(1996), 23–41) generalized the formula for sums of products of any number of Bernoulli numbers, but it is not easy to prove the generalized formula forq-Bernoulli numbers. In this paper we give aq-formula in the case of twoq-Bernoulli numbers.