Abstract
We give explicitly a class of polynomials with complex coefficients of degreen which deviate least from zero on [−1, 1] with respect to the max-norm among all polynomials which have the same,m + 1, 2m ≤n, first leading coefficients. Form=1, we obtain the polynomials discovered by Freund and Ruschewyh. Furthermore, corresponding results are obtained with respect to weight functions of the type 1/√ρl, whereρl is a polynomial positive on [−1, 1].
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Communicated by Edward B. Saff.
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Peherstorfer, F. Explicit generalized zolotarev polynomials with complex coefficients. Constr. Approx 13, 261–269 (1997). https://doi.org/10.1007/BF02678468
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DOI: https://doi.org/10.1007/BF02678468