On the asymptotic behaviour of the Titchmarsh–Weyl $m$-function

The asymptotic expansion
$$ m(z)=\frac{i}{\sqrt z}+\sum_{k=1}^{n+1}a_k(-z)^{-(k+2)/2}+\varepsilon_n(z),\quad \varepsilon_n(z)=o(|z|^{-(k+3)/2}), $$
valid outside any angle $|{\operatorname{tg}\theta}|<\varepsilon$, $\varepsilon>0$, is obtained for the Weyl–Titchmarsh function of the Sturm-Liouville problem on the half-axis with potential $g(x)\in C^n[0,\delta)$.