Geodesic
Asymptotic Behavior of Semiclassical Polynomials of Joint Orthogonality of Bessel Type
Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 483-495

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, for Bessel polynomials, we obtain asymptotics uniform on compact sets inside some domain and uniform on compact subsets of some curves.
Mots-clés : Bessel polynomial, Hermite–Padé approximation
Keywords: Pearson equation, Darboux method, Riemann surface, holomorphic function, generating function. 
R. È. Akhmedov. Asymptotic Behavior of Semiclassical Polynomials of Joint Orthogonality of Bessel Type. Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 483-495. http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a0/
@article{MZM_2008_84_4_a0,
     author = {R. \`E. Akhmedov},
     title = {Asymptotic {Behavior} of {Semiclassical} {Polynomials} of {Joint} {Orthogonality} of {Bessel} {Type}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--495},
     year = {2008},
     volume = {84},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a0/}
}
TY  - JOUR
AU  - R. È. Akhmedov
TI  - Asymptotic Behavior of Semiclassical Polynomials of Joint Orthogonality of Bessel Type
JO  - Matematičeskie zametki
PY  - 2008
SP  - 483
EP  - 495
VL  - 84
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a0/
LA  - ru
ID  - MZM_2008_84_4_a0
ER  - 
%0 Journal Article
%A R. È. Akhmedov
%T Asymptotic Behavior of Semiclassical Polynomials of Joint Orthogonality of Bessel Type
%J Matematičeskie zametki
%D 2008
%P 483-495
%V 84
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a0/
%G ru
%F MZM_2008_84_4_a0

[1] A. A. Gonchar, E. A. Rakhmanov, “O skhodimosti sovmestnykh approksimatsii Pade dlya sistemy funktsii markovskogo tipa”, Teoriya chisel, matematicheskii analiz i ikh prilozheniya, Tr. MIAN, 157, Nauka, M., 1981, 31–48 | MR | Zbl

[2] J. Nuttall, “Asymptotics of diagonal Hermite–Padé polynomials”, J. Approx. Theory, 42:4 (1984), 299–386 | DOI | MR | Zbl

[3] J. Nuttall, “Hermite–Padé approximants to functions meromorphic on a Riemann surface”, J. Approx. Theory, 32:3 (1981), 233–240 | DOI | MR | Zbl

[4] A. I. Aptekarev, H. Stahl, “Asymptotics of Hermite–Padé polynomials”, Progress in Approximation Theory (Tampa, FL, March 1990), Springer Ser. Comput. Math., 19, Springer-Verlag, Berlin–New York, 1992, 127–164 | MR

[5] P. K. Cyetin, Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1976 | MR | Zbl

[6] G. Cege, Ortogonalnye mnogochleny, Fizmatgiz, M., 1962 | MR | Zbl

[7] A. I. Aptekarev, F. Marcellan, I. A. Rocha, “Semiclassical multiple orthogonal polynomials and the properties of Jacobi–Bessel polynomials”, J. Approx. Theory, 90:1 (1997), 117–146 | DOI | MR | Zbl

[8] P. Appell, “Sur une suite des polynômes ayant toutes leur racines réelles”, Arch. Math. Phys., 1:3 (1901), 69–71 | Zbl

[9] N. Chosh, “On a generalization of Legendre polynomials”, Bull. Calcutta Math. Soc., 21 (1929), 144–154

[10] G. K. Engelis, “O polinomakh, zadannykh formuloi Rodriga”, Uchenye zapiski Latv. GU, 20:3 (1958), 137–143 | MR

[11] V. A. Kalyagin, “Ob odnom klasse polinomov, opredelyaemykh dvumya sootnosheniyami ortogonalnosti”, Matem. sb., 110:4 (1979), 609–627 | MR | Zbl

[12] V. Kaliaguine, A. Ronveaux, “On a system of “classical” polynomials of simultaneous orthogonality”, J. Comput. Appl. Math., 67:2 (1996), 207–217 | DOI | MR | Zbl

[13] V. N. Sorokin, “O sovmestnykh approksimatsiyakh Pade v sluchae konechnykh i beskonechnykh intervalov”, Izv. vuzov. Matem., 8 (1984), 45–52 | MR | Zbl

[14] V. N. Sorokin, “Obobschenie klassicheskikh ortogonalnykh mnogochlenov i skhodimost sovmestnykh approksimatsii Pade”, Trudy sem. im. I. G. Petrovskogo, 1986, no. 11, 125–165 | MR | Zbl

[15] V. N. Sorokin, “Asimptoticheskoe povedenie lineinykh form s polinomialnymi koeffitsientami dlya nekotorykh funktsii stiltesovskogo tipa”, Sib. matem. zhurn., 27:1 (1986), 157–169 | MR | Zbl

[16] V. N. Sorokin, “O sovmestnykh approksimatsiyakh Pade funktsii stiltesovskogo tipa”, Sib. matem. zhurn., 31:5 (1990), 128–137 | MR | Zbl

[17] E. M. Hikishin, V. N. Sorokin, Ratsionalnye approksimatsii i ortogonalnost, Nauka, M., 1988 | MR | Zbl