Approximate zolotarev polynomials

AbstractThe Zolotarev polynomials are of importance in theoretical and practical approximation. They are connected with elliptic functions, thus an explicit description presents difficulties. We exhibit polynomials of simple structure which have similar approximation properties to those of the Zolotarev polynomials and therefore can replace them in many cases. Our error estimates extend and improve results due to Bernstein and Reddy. Further we discuss generalizations and the relation to the Carathéodory-Fejér approximation