On Gaussian Quadrature Formulas for the Chebyshev Weight Original Research Article

This paper shows that the Chebyshev weightw(x)=(1−x2)−1/2is the only weight having the property (up to a linear transformation): For each fixedn, the solutions of the extremal problem ∫1−1 |∏nk−1 (x−xk)|m w(x) |∏n−1k=1 (x−yk)|p (1−x2)p/2 w(x) dx=minp=xn+…, Q=xn−1+… ∫1−1 |P(x)|m |Q(x)|p (1−x2)p/2 w(x) dxare the same for anym, p⩾1.