Introduction and Results

Abstract

Let I be a finite or infinite interval and let w: I → [0, ∞) be measurable with all power moments

$$ \int_{I} {{x^{n}}w(x)dx,{\text{ n = 0, 1, 2, 3,}}...} "$$

finite. Then we call w a weight and may define orthonormal polynomials

$$ {p_{n}}(x) = {p_{n}}(w,{\text{ }}x) = {\gamma _{n}}(w){x^{n}} + \cdot \cdot \cdot ,{\gamma _{n}}(w) > 0, "$$

satisfying

$$ \int_{I} {{p_{n}}{p_{m}}w = {d_{{mn}}},m, n = 0, 1, 2,... .} "$$