On p-adic q-L-functions and sums of powers

We give an explicit p-adic expansion of ∑∗j=1npqj/[j]r as a power series in n which generalizes the formula of Andrews (Discrete Math. 204 (1999) 15). Indeed, this is a q-analogue result due to Washington (J. Number Theory 69 (1998) 50), corresponding to the case q=1.