Using the notation of the quasiasymptotic expansion of a tempered distribution at $\infty$ an ordinary asymptotic expansion of the Stieltjes transformation of function from $L^1_{\operatorname{loc}}(0,\infty)$ is obtained with the ordinary, asymptotic expansion of the form $\sum_{i=1}^{\infty}\frac{a_i}{t^i}$, $t\to\infty$.