Geodesic
Expansions in series and the rate of rational approximations for holomorphic functions with analytic singularities
Sbornik. Mathematics, Tome 22 (1974) no. 2, pp. 323-332
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It is proved that for functions holomorphic in the complement of an analytic subset of $\mathbf C^N$ the best rational approximation converges faster than any geometric progression. Bibliography: 3 titles. 
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     title = {Expansions in series and the rate of rational approximations for holomorphic functions with analytic singularities},
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E. M. Chirka. Expansions in series and the rate of rational approximations for holomorphic functions with analytic singularities. Sbornik. Mathematics, Tome 22 (1974) no. 2, pp. 323-332. http://geodesic.mathdoc.fr/item/SM_1974_22_2_a8/

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

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

[3] A. A. Gonchar, “Lokalnoe uslovie odnoznachnosti analiticheskikh funktsii neskolkikh peremennykh”, Matem. sb., 93(135):2 (1974), 296–313 | MR | Zbl