Geodesic
The poles of Tchebycheff rational approximations and meromorphic extension of~functions
Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 379-391

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A characterization is given for an $m$-meromorphic continuation of a continuous function $f$ on the segment $[-1,1]$, in terms of the asymptotic behavior of the finite poles of the $m$th row of the table of Tchebycheff rational approximants to $f$. 
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     author = {V. A. Prokhorov},
     title = {The poles of {Tchebycheff} rational approximations and meromorphic extension of~functions},
     journal = {Sbornik. Mathematics},
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     volume = {69},
     number = {2},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_69_2_a3/}
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V. A. Prokhorov. The poles of Tchebycheff rational approximations and meromorphic extension of~functions. Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 379-391. http://geodesic.mathdoc.fr/item/SM_1991_69_2_a3/