On Gaussian quadrature formulas for the Chebyshev weight

This paper shows that the Chebyshev weight w(x) = (1 - x(2))(-1/2) is the only weight having the property (up to a linear transformation): For each fixed n, the solutions of the extremal problem integral(-1)(1)\Pi(k-1)(n) (x-x(k))/(m)w(x)\Pi(k=1)(n-1)(x - y(k))\(p) (1 - x(2))(p/2) w(x) dx = min(p=xn+..., Q = xn-1 +...) integral(-1)(1)\P(x)\(m)\Q(x)\(p) (1 - x(2))(p/2) w(x)dx are the same for any m, p greater than or equal to 1. (C) 1999 Academic Press.