Geodesic
On Montessus de Ballore's theorem for rational approximants of orthogonal expansions
Sbornik. Mathematics, Tome 42 (1982) no. 3, pp. 399-411 
S. P. Suetin. On Montessus de Ballore's theorem for rational approximants of orthogonal expansions. Sbornik. Mathematics, Tome 42 (1982) no. 3, pp. 399-411. http://geodesic.mathdoc.fr/item/SM_1982_42_3_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The analogue of a classical theorem of Montessus de Ballore for meromorphic functions given by their Fourier expansion with respect to orthogonal polynomials is proved. Bibliography: 9 titles.

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

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

[3] Suetin S. P., “O skhodimosti ratsionalnykh approksimatsii polinomialnykh razlozhenii v oblastyakh meromorfnosti zadannoi funktsii”, Matem. sb., 105 (147) (1978), 413–430 | MR | Zbl

[4] Fleischner J., “Nonlinear Pade approximants for Legendre series”, J. Math, and Phys., 14:2 (1973), 246–248 | DOI | MR

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

[6] Segë G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[7] Suetin S. P., “O teoreme Montessu de Bolora dlya nelineinykh approksimatsii Pade ortogonalnykh razlozhenii i ryadov Fabera”, DAN SSSR, 253:6 (1980), 1322–1325 | MR | Zbl

[8] Shabat B. V., Vvedenie v kompleksnyi analiz, Ch. II, Nauka, M., 1976 | MR

[9] Smirnov V. I., Lebedev N. A., Konstruktivnaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., L., 1964 | MR