Geodesic
Generalized Padé approximants and meromorphic continuation of functions
Sbornik. Mathematics, Tome 37 (1980) no. 3, pp. 337-348 
R. K. Kovacheva. Generalized Padé approximants and meromorphic continuation of functions. Sbornik. Mathematics, Tome 37 (1980) no. 3, pp. 337-348. http://geodesic.mathdoc.fr/item/SM_1980_37_3_a2/
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     title = {Generalized {Pad\'e} approximants and meromorphic continuation of functions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this work, a converse theorem relating to interpolatory sequences of rational functions with a fixed number of free poles is proved. This theorem gives a measure of the domain of $m$-meromorphy of the given function in terms of the speed of convergence of the free poles of its rational approximants. Bibliography: 8 titles.

[1] Dzh. A. Uolsh, Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi ploskosti, IL, Moskva, 1961

[2] T. Bagby, “On interpolating by rational functions”, Duke Math. J., 36:1 (1969), 95–104 | DOI | MR | Zbl

[3] A. A. Gonchar, “O skhodimosti obobschennykh approksimatsii Pade meromorfnykh funktsii”, Matem. sb., 98(104) (1975), 564–577 | Zbl

[4] J. Hadamard, “Essai sur l'etude des fonctions donnees par leur developpement de Taylor”, J. Math., 418 (1892), 101–186

[5] R. de Montessus de Ballore, “Sur le fractions continues algebriques”, Bull. Soc. Math. France, 301 (1902), 28–36 | MR

[6] E. B. Saff, “An extension of Montessus de Ballores theorem on the convergence of interpolating rational functions”, J. Approx. Theory, 6 (1972), 63–68 | DOI | MR

[7] A. A. Gonchar, “O skhodimosti approksimatsii Pade dlya nekotorykh klassov meromorfnykh funktsii”, Matem. sb., 97(139) (1975), 607–629 | Zbl

[8] R. K. Kovacheva, “O kriterii $m$-meromorfnosti”, Materialy Mezhdunarodnoi konferentsii po konstruktivnoi teorii funktsii (Blagoevgrad, Bolgariya, 31.V.-4.VI.1977 g.)