Geodesic
On the Convergence of Continued T-Fractions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 36-51

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It is shown that a continued $\mathrm T$-fraction converges on the set $\{|z|$. Formulas (exact in a certain sense) for evaluating the radii $R_1$ and $R_2$ of these disks are given. For a $\mathrm T$-fraction with limit-periodic coefficients, a cut $\Gamma$ on the complex plane is explicitly specified such that this $\mathrm T$-fraction converges outside this cut. It is shown that the meromorphic function represented by this $\mathrm T$-fraction cannot be meromorphically continued (as a single-valued function) across any arc lying on $\Gamma$. 
@article{TM_2001_235_a1,
     author = {V. I. Buslaev},
     title = {On the {Convergence} of {Continued} {T-Fractions}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {36--51},
     publisher = {mathdoc},
     volume = {235},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_235_a1/}
}
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V. I. Buslaev. On the Convergence of Continued T-Fractions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 36-51. http://geodesic.mathdoc.fr/item/TM_2001_235_a1/