Geodesic
On the convergence of rational approximations to polynomial expansions in domains of meromorphy of a given function
Sbornik. Mathematics, Tome 34 (1978) no. 3, pp. 367-381 
S. P. Suetin. On the convergence of rational approximations to polynomial expansions in domains of meromorphy of a given function. Sbornik. Mathematics, Tome 34 (1978) no. 3, pp. 367-381. http://geodesic.mathdoc.fr/item/SM_1978_34_3_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We establish analogs of the theorem of Montessus de Ballore for rational approximations (of the type of the Padé approximants) to series of orthogonal polynomials and of Faber polynomials. Bibliography: 11 titles.

[1] J. T. Holdeman, “A Method for the Approximation of Functions defined by Formal Series Expansions in Orthogonal Polinomials”, Math, of Comp., 23(106), April (1969), 275–287 | DOI | MR | Zbl

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

[3] G. A. Baker Jr., The Pade Approximant in Theoretical Physics, eds. Baker and GammeL, Academic Press, New York, 1970 | MR

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

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

[6] E. A. Rakhmanov, “Ob asimptotike otnosheniya ortogonalnykh mnogochlenov”, Matem. sb., 103(145) (1977), 237–252 | Zbl

[7] G. Sege, Ortogonalnye mnogochleny, Fizmatgiz, Moskva, 1962

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

[9] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, izd-vo “Nauka”, Moskva, 1966 | MR

[10] V. V. Vavilov, “O skhodimosti approksimatsii Pade meromorfnykh funktsii”, Matem. sb., 101(143) (1976), 44–56 | MR | Zbl

[11] V. I. Smirnov, N. A. Lebedev, Konstruktivnaya teoriya funktsii kompleksnogo peremennogo, izd-vo “Nauka”, Moskva–Leningrad, 1964 | MR | Zbl