The behaviour of the Stieltjes transformation at the origin is investigated for a function $f$ from $L^1_{\operatorname{loc}}$, $\operatorname{supp}f\subset[0,\infty)$ with the asymptotic expansion of the form \[ um^ıfty_{i=p}a_it^i,\quad to0. \] This new result follows from the known one for the asymptotic expansion at $\infty$. Since the notion of the quasiasymptotic expansion of distributions is used, the result can be formulated for the distributional Stieltjes transformation of distributions.