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  "body": "\n## Summary\n\nZolotarev polynomials solve an extremal problem close to the one solved by [[Chebyshev polynomials|M6EAR1JHPP]].\nAmong the real polynomials of degree $n$ whose two leading coefficients are fixed, they have the least maximum absolute value on $[-1, 1]$.\nYegor Zolotarev studied them in the nineteenth century, and in general they are expressed through elliptic functions.\n\n## Explanations\n\n### L1 human\n\nThe Chebyshev problem fixes only the leading coefficient and asks for the polynomial that stays smallest on $[-1, 1]$.\nThe Zolotarev problem fixes the first two coefficients and asks the same question.\nWhen the second coefficient is $0$, the answer is still the scaled Chebyshev polynomial $2^{1-n} T_n$.\nWhen the second coefficient is large, the optimal polynomial still wiggles between two equal bounds, but its shape is more complicated.\n",
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