q-Extension of Fubini Numbers

In this paper we define a q -extension of Fubini numbers which we call q -Fubini numbers, and generalized q -Fubini numbers of order r. Using the p -adic Laplace transform and p -adic integration, we obtain these numbers as moments of appropriate p -adicmeasures. Then we establish some identities and congruences for these numbers. We establish also a relationship between generalized q -Fubini numbers of order r and q -Fubini numbers. Further, as done in previous works we introduce a concept of generalized q -Fubini numbers, attached to a continuous p ℓ ℤ p -invariant function ψ defined on ℤ p . These numbers are also the moments of appropriate p -adic measures, we obtain identities and congruences which generalize those associated to q -Fubini numbers.