Zolotarev polynomials

Summary

Zolotarev polynomials solve an extremal problem close to the one solved by Chebyshev polynomials. Among the real polynomials of degree $n$ whose two leading coefficients are fixed, they have the least maximum absolute value on $[-1, 1]$. Yegor Zolotarev studied them in the nineteenth century, and in general they are expressed through elliptic functions.