Let \(\overline{p}(n)\) denote the overpartition function, and for \(j\in \mathbb {N}\) , \(\Delta ^r_j\) denote the r-fold applications of the shifted difference operator \(\Delta _j\) defined by \(\Delta _j(a)(n):=a(n)-a(n-j)\) . The main goal of this paper is to derive an asymptotic expansion of \(\Delta ^r_j(\overline{p})(n)\) with an effective error bound which subsequently gives an answer to a problem of Wang, Xie, and Zhang. In order to get the asymptotics of \(\Delta ^r_j(\overline{p})(n)\) , we derive an asymptotic expansion of the shifted overpartition function \(\overline{p}(n+k)\) for any integer \(k\ne 0\) .
