Various important sets of polynomials (Legendre, Chebyshev, etc.) are orthogonal over some real interval with some weighting. Are there known families of polynomials that are orthogonal over other curves in the complex plane?
For instance, I would like a basis for the polynomials of degree n that is orthogonal over, say, the circle
$$-1 + \exp(it)$$
for $0\le t< 2\pi$.