Geodesic
The poles of Tchebycheff rational approximations and meromorphic extension of functions
Sbornik. Mathematics, Tome 69 (1991) no. 2, pp. 379-391 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {The poles of {Tchebycheff} rational approximations and meromorphic extension of~functions},
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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/

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