Geodesic
Convergence of Padé approximants of Stieltjes type meromorphic functions and comparative asymptotics for orthogonal polynomials
Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 207-227 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theorem is proved on the uniform convergence of diagonal Padé approximants for Stieltjes type meromorphic functions (with a finite number of poles). Bibliography: 13 titles. 
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     author = {G. L. Lopes},
     title = {Convergence of {Pad\'e} approximants of {Stieltjes} type meromorphic functions and comparative asymptotics for orthogonal polynomials},
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     year = {1989},
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G. L. Lopes. Convergence of Padé approximants of Stieltjes type meromorphic functions and comparative asymptotics for orthogonal polynomials. Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 207-227. http://geodesic.mathdoc.fr/item/SM_1989_64_1_a12/

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[3] Lopes G., “Skhodimost approksimatsii Pade dlya meromorfnykh funktsii stiltesovskogo tipa”, Matem. sb., 111(153) (1980), 308–316 | MR

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

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[7] Lopes G., “Ob asimptotike otnosheniya ortogonalnykh mnogochlenov i skhodimosti mnogotochechnykh approksimatsii Pade”, Matem. sb., 128(170) (1985), 216–229 | MR

[8] Mate A., Nevai P., Totik V., “Asymptotics for the ratio of leading coefficients of orthogonal polynomials on the unit circle”, Constr. Appr., 1 (1985), 63–69 | DOI | MR | Zbl

[9] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR

[10] Gonchar A. A., “O skhodimosti obobschennykh approksimatsii Pade meromorfnykh funktsii”, Matem. sb., 98(140) (1975), 564–578

[11] Geronimus Ya. L., Mnogochleny, ortogonalnye na okruzhnosti i na otrezke, Fizmatgiz, M., 1958 | Zbl

[12] Lopes G., “Uslovie skhodimosti mnogotochechnykh approksimatsii Pade dlya funktsii stiltesovskogo tipa”, Matem. sb., 107(149) (1978), 69–83 | MR | Zbl

[13] Uolsh Dzh., Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, IL, M., 1961 | MR