 Chebyshev minimax polynomial with exterior normalization

For $0<a<b$, the displayed polynomial minimizes ${\max }_{t\in [a,b]}|p(t)|$ among real polynomials of degree at most $k$ with $p(0)=1$. Its $k+1$ alternating extremal values prove the assertion: a strictly smaller competitor would make the difference change sign in each consecutive extremal interval and also vanish at zero outside $[a,b]$, giving too many roots. The normalizing factor makes either the monic or the usual Chebyshev polynomial convention give the same ratio. For $\kappa =b/a$ and $q=(\sqrt{\kappa }-1)/(\sqrt{\kappa }+1)$, its maximum is $2q^k/(1+q^{2k})$. This yields an error bound for polynomial acceleration of Richardson iteration.