On Turán Quadrature Formulas for the Chebyshev Weight Original Research Article

As we know, the Chebyshev weightw(x)=(1−x2)−1/2has the property: For each fixedn, the solutions of the extremal problem ∫1−1[∏nk=1(x−xk)]m w(x) dx=minP=xn+…∫1−1 P(x)m w(x) dxfor every evenmare the same. This paper proves that the Chebyshev weight is the only weight having this property (up to a linear transformation).