Abstract
In this paper, for Bessel polynomials, we obtain asymptotics uniform on compact sets inside some domain and uniform on compact subsets of some curves.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. A. Gonchar and E. A. Rakhmanov, “On the convergence of simultaneous Padé approximations for systems of functions of Markov type,” in Trudy Mat. Inst. Steklov Vol. 157: Number Theory, Mathematical Analysis, and Their Applications (Nauka, Moscow, 1981), pp. 31–48. [in Russian].
J. Nuttall, “Asymptotics of diagonal Hermite-Padé polynomials,” J. Approx. Theory 42(4), 299–386 (1984).
J. Nuttall, “Hermite-Padé approximants to functions meromorphic on a Riemann surface,” J. Approx. Theory 32(3), 233–240 (1981).
A. I. Aptekarev and H. Stahl, “Asymptotics of Hermite-Padé polynomials,” in Progress in Approximation Theory, Springer Ser. Comput. Math., Tampa, FL, March 1990 (Springer-Verlag, Berlin-New York, 1992), Vol. 19, pp. 127–164.
P. K. Suetin, Classical Orthogonal Polynomials (Nauka, Moscow, 1976) [in Russian].
G. Szegö, Orthogonal Polynomials (Colloquium Publ., Vol. XXIII, Amer. Math. Soc., Providence, RI, 1959; Fizmatgiz,Moscow, 1962).
A. I. Aptekarev, F. Marcellan, and I. A. Rocha, “Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials,” J. Approx. Theory 90(1), 117–146 (1997).
P. Appell, “Sur une suite de polynômes ayant toutes leur racines réelles,” Arch. Math. Phys. 1(3), 69–71 (1901).
N. Chosh, “On a generalization of Legendre polynomials,” Bull. Calcutta Math. Soc. 21, 144–154 (1929).
G. K. Engelis, “Polynomials given by their Rodrigues formula,” Latvijas Valsts Univ. Zinātn. Raksti, 20(3), 137–143 (1958).
V. A. Kalyagin, “On a class of polynomials defined by two orthogonality relations,” Mat. Sb. 110(4), 609–627 (1979) [Math. USSR-Sb. 38, 563–580 (1981)].
V. Kaliaguine and A. Ronveaux, “On a system of “classical” polynomials of simultaneous orthogonality,” J. Comput. Appl.Math. 67(2), 207–217 (1996).
V. N. Sorokin, “On simultaneous Padé approximations in case of finite and infinite intervals,” Izv. Vyssh. Uchebn. Zaved.Mat. 8, 45–52 (1984).
V. N. Sorokin, “A generalization of classical orthogonal polynomials and the convergence of simultaneous Padé approximants,” Tr. Semin. Im. I. G. Petrovskogo, No. 11, 125–165 (1986) [J. Sov.Math. 45 (6), 1461–1499 (1989)].
V. N. Sorokin, “Asymptotic behavior of linear forms with polynomial coefficients for some functions of Stieltjes type,” Sibirsk. Mat. Zh. 27(1), 157–169 (1986) [SiberianMath. J. 27 (1), 126–136 (1986)].
V. N. Sorokin, “Simultaneous Padé approximants of functions of Stieltjes type,” Sibirsk. Mat. Zh. 31(5), 128–137 (1990) [SiberianMath. J. 31 (5), 809–817 (1990)].
E. M. Nikishin and V. N. Sorokin, Rational Approximations and Orthogonality (Nauka, Moscow, 1988) [in Russian].
Author information
Authors and Affiliations
Additional information
Original Russian Text © R. É. Akhmedov, 2008, published in Matematicheskie Zametki, 2008, Vol. 84, No. 4, pp. 483–495.
Rights and permissions
About this article
Cite this article
Akhmedov, R.É. Asymptotic behavior of semiclassical polynomials of joint orthogonality of Bessel type. Math Notes 84, 453–464 (2008). https://doi.org/10.1134/S0001434608090174
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434608090174