Chebyshev polynomial of the second kind
= Chebyshev polynomial of the second kind
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The Chebyshev polynomial of the second kind is defined by
$$
U_n(\cos\theta)=\frac{\sin((n+1)\theta)}{\sin\theta}.
$$
It is orthogonal on $[-1,1]$ with weight $\sqrt{1-x^2}$ and has roots $\cos(j\pi/(n+1))$ for $1\leq j\leq n$.