8.901 Suppose that w(x) is a nonnegative real function of a real variable x. Let (a, b) be a fixed interval on the x-axis. Let us suppose further that, for n = 0, 1, 2, …, the integral
exists and that the integral
is positive. In this case, there exists a sequence of polynomials p0(x), p1(x), …, pn(x), …, that is uniquely determined by the following conditions:
1. pn(x) is a polynomial of degree n and the coefficient of xn in this polynomial is positive.
2. The polynomials ...