EXPLICIT GENERALIZED ZOLOTAREV POLYNOMIALS WITH COMPLEX COEFFICIENTS

We give explicitly a class of polynomials with complex coefficients of degree n which deviate least from zero on [-1, 1] with respect to the max-norm among all polynomials which have the same, m + 1, 2m less th an or equal to n, first leading coefficients. For m = 1,we obtain the polynomials discovered by Freund and Ruscheweyh. Furthermore, correspo nding results are obtained with respect to weight functions of the typ e 1/root rho(l), where rho(l) is a polynomial positive on [-1, 1].