Geodesic
Asymptotics of orthogonal polynomials in a neighborhood of the endpoints of the interval of orthogonality
Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 35-50 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The well-known Mehler–Heine asymptotic formula for the classical Jacobi polynomials is extended to broader classes of orthogonal polynomials. 
@article{SM_1993_76_1_a2,
     author = {A. I. Aptekarev},
     title = {Asymptotics of orthogonal polynomials in a~neighborhood of the~endpoints of the~interval of orthogonality},
     journal = {Sbornik. Mathematics},
     pages = {35--50},
     year = {1993},
     volume = {76},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_76_1_a2/}
}
TY  - JOUR
AU  - A. I. Aptekarev
TI  - Asymptotics of orthogonal polynomials in a neighborhood of the endpoints of the interval of orthogonality
JO  - Sbornik. Mathematics
PY  - 1993
SP  - 35
EP  - 50
VL  - 76
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1993_76_1_a2/
LA  - en
ID  - SM_1993_76_1_a2
ER  - 
%0 Journal Article
%A A. I. Aptekarev
%T Asymptotics of orthogonal polynomials in a neighborhood of the endpoints of the interval of orthogonality
%J Sbornik. Mathematics
%D 1993
%P 35-50
%V 76
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1993_76_1_a2/
%G en
%F SM_1993_76_1_a2
A. I. Aptekarev. Asymptotics of orthogonal polynomials in a neighborhood of the endpoints of the interval of orthogonality. Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 35-50. http://geodesic.mathdoc.fr/item/SM_1993_76_1_a2/

[1] Sege G., Ortogonalnye mnogochleny, Fizmatizdat, M., 1962

[2] Levitan B. M., Sargsyan I. S., Vvedenie v spektralnuyu teoriyu, Nauka, M., 1970 | MR | Zbl

[3] Badkov V. M., “Asimptoticheskoe povedenie ortogonalnykh mnogochlenov”, Matem. sb., 109(151) (1979), 46–59 | MR | Zbl

[4] Mate A., Nevai P., Totik V., “What is beyond Szegö's theory of orthogonal polynomials?”, Lecture Notes in Math., 1105, 1984, 502–510 | MR | Zbl

[5] Rakhmanov E. A., “Ob asimptoticheskikh svoistvakh mnogochlenov, ortogonalnykh na okruzhnosti s vesami, ne udovletvoryayuschimi usloviyu Sege”, Matem. sb., 130(172) (1986), 151–169 | MR