Geodesic
On the asymptotic behaviour of the Titchmarsh–Weyl $m$-function
Izvestiya. Mathematics, Tome 36 (1991) no. 3, pp. 487-496 
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/
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     author = {A. A. Danielyan and B. M. Levitan},
     title = {On the asymptotic behaviour of the {Titchmarsh{\textendash}Weyl} $m$-function},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_3_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $g(x)\in C^n[0,\delta)$.

[1] Levitan B. M., Sargsyan I. S., Vvedenie v spektralnuyu teoriyu, Nauka, M., 1970 | MR | Zbl

[2] Harris B. J., “The Asymptotic form of the Titchmarsh–Weyl $M$-function”, J. London Math. Soc., 30 (1984), 110–118 | DOI | MR | Zbl

[3] Levitan B. M., “Ob odnoi spetsialnoi tauberovoi teoreme”, Izv. AN SSSR. Ser. matem., 17:3 (1953), 269–284 | MR | Zbl

[4] Everitt W. A., “On a property of the $M$-coefficient of a second-order linear differential equation”, J. London Math. Soc., 4 (1972), 443–457 | DOI | MR | Zbl

[5] Everitt W. A., Halvorsen S. G., “On a asymptotic form of the Titchmarsh–Weyl $m$-coefficient”, Applicable analysis, 8 (1978), 153–169 | DOI | MR | Zbl

[6] Atkinson F. A., “On the location of the Weyl circles”, Proc. Roy. Soc. Edinburg. Sec. A., 88 (1981), 345–356 | MR | Zbl

[7] Levitan B. M., Obratnye zadachi Shturma–Liuvillya, Nauka, M., 1984 | MR

[8] Vatson G. N., Teoriya besselevykh funktsii, IL, M., 1949