Abstract
Asymptotic estimates are obtained in a uniform metric and in the L p metrics (p ≥ 2) for the difference between Chebyschev polynomials with a discrete argument and Legendre polynomials, under simultaneous passage to infinity of the degree of the polynomials and the number of lattice nodes at which the Chebyschev polynomials are defined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
I. K. Daugavet, An Introduction to the Theory of Approximate Functions [in Russian], Leningrad (1977).
V. I. Krylov, Approximation of Integrals [in Russian], Moscow (1967).
Yu. Lyuk, Special Functions and Their Approximation [in Russian], Moscow (1980).
A. F. Nikiforov, S. K. Suslov, and V. B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable [in Russian], Moscow (1985).
G. Szegö, Orthogonal Multinomials [in Russian], Moscow (1962).
M. Abramowitz and I. Stigan (eds.), Handbook of Special Functions [in Russian], Moscow (1979).
Author information
Authors and Affiliations
Additional information
Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 37–43, 1989.
Rights and permissions
About this article
Cite this article
Min'ko, A.A. A limiting relation between Chebyschev polynomials with a discrete argument and Legendre polynomials. J Math Sci 67, 3059–3063 (1993). https://doi.org/10.1007/BF01098140
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01098140