Geodesic
On the asymptotic behaviour of the Titchmarsh--Weyl $m$-function
Izvestiya. Mathematics , Tome 36 (1991) no. 3, pp. 487-496

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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 $g(x)\in C^n[0,\delta)$. 
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     author = {A. A. Danielyan and B. M. Levitan},
     title = {On the asymptotic behaviour of the {Titchmarsh--Weyl} $m$-function},
     journal = {Izvestiya. Mathematics },
     pages = {487--496},
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     number = {3},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_3_a1/}
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A. A. Danielyan; B. M. Levitan. On the asymptotic behaviour of the Titchmarsh--Weyl $m$-function. Izvestiya. Mathematics , Tome 36 (1991) no. 3, pp. 487-496. http://geodesic.mathdoc.fr/item/IM2_1991_36_3_a1/