A limiting relation between Chebyschev polynomials with a discrete argument and Legendre polynomials

Asymptotic estimates are obtained in a uniform metric and in the L_pmetrics (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.Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 37–43, 1989.