Geodesic
Poles of diagonal Padé approximants and the analytic continuation of functions
Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 255-266 
A. A. Gonchar; K. N. Lungu. Poles of diagonal Padé approximants and the analytic continuation of functions. Sbornik. Mathematics, Tome 39 (1981) no. 2, pp. 255-266. http://geodesic.mathdoc.fr/item/SM_1981_39_2_a6/
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     author = {A. A. Gonchar and K. N. Lungu},
     title = {Poles of diagonal {Pad\'e} approximants and the analytic continuation of functions},
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     year = {1981},
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     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_39_2_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the authors study the connection between the asymptotic behavior of the poles of the diagonal Padé approximants of a function $f$ (given by its power series expansion) and the possibility of analytic continuation of $f$ into a corresponding domain. Bibliography: 8 titles.

[1] O. Perron, Die Lehre von den Kettenbruchen, Band II, Teubner, Stuttgart, 1957 | MR | Zbl

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

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

[4] Dzh. L. Uolsh, Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, IL, Moskva, 1961 | MR

[5] A. A. Gonchar, “Lokalnoe uslovie odnoznachnosti analiticheskikh funktsii”, Matem. sb., 89(131) (1972), 148–164 | Zbl

[6] A. A. Gonchar, “O skhodimosti approksimatsii Pade”, Matem. sb., 92(134) (1973), 152–164 | Zbl

[7] A. A. Gonchar, “O skhodimosti obobschennykh approksimatsii Pade meromorfnykh funktsii”, Matem. sb., 98(140) (1975), 564–577 | Zbl

[8] E. A. Rakhmanov, “O skhodimosti diagonalnykh approksimatsii Pade”, Matem. sb., 108(150) (1977), 272–291