An explicit univariate and radical parametrization of the sextic proper Zolotarev polynomials in power form

Abstract

The problem to determine an explicit one-parameter power form representation of the proper Zolotarev polynomials of degree n and with uniform norm 1 on [-1,1] can be traced back to P. L. Chebyshev. It turned out to be complicated, even for small values of n. Such a representation was known to A. A. Markov (1889) for n = 2 and n = 3. But already for n = 4 it seems that nobody really believed that an explicit form can be found. As a matter of fact it was, by V. A. Markov in 1892, as A. Shadrin put it in 2004. About 125 years passed before an explicit form for the next higher degree, n = 5, was found, by G. Grasegger and N. Th. Vo (2017). In this paper we settle the case n = 6.

Rack H., Vajda R. (2019) "An explicit univariate and radical parametrization of the sextic proper Zolotarev polynomials in power form " Dolomites Research Notes on Approximation, 12(1), 43-50. DOI: 10.14658/PUPJ-DRNA-2019-1-5  
Year of Publication
2019
Journal
Dolomites Research Notes on Approximation
Volume
12
Issue Number
1
Start Page
43
Last Page
50
Date Published
05/2019
ISSN Number
2035-6803
Serial Article Number
5
DOI
10.14658/PUPJ-DRNA-2019-1-5
Issue
Section
Articles