Geodesic
On the poles of the $m$th row of the Padé table
Sbornik. Mathematics, Tome 45 (1983) no. 4, pp. 423-429 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that the $m$-meromorphic extensions of $f(z)=\sum\limits_{k=0}^\infty f_kz^k$ can be described in terms of the asymptotic distribution of the poles of the $m$th row of the Padé table of $f(z)$. Bibliography: 2 titles. 
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     author = {V. I. Buslaev},
     title = {On the poles of the $m$th row of the {Pad\'e} table},
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     year = {1983},
     volume = {45},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_4_a0/}
}
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V. I. Buslaev. On the poles of the $m$th row of the Padé table. Sbornik. Mathematics, Tome 45 (1983) no. 4, pp. 423-429. http://geodesic.mathdoc.fr/item/SM_1983_45_4_a0/

[1] Wall H. S., Analytic Theory of continued Fractions, Van Nostrand, New York, 1948 | MR | Zbl

[2] Gonchar A. A., “Polyusy strok tablitsy Pade i meromorfnoe prodolzhenie funktsii”, Matem. sb., 115 (157) (1981), 590–613 | MR | Zbl