Orthogonal polynomials for exponential weights x^2ρe^-2Q(x) on [0,d)

Let I = [0, d), where d is finite or infinite. Let W_ρ (x) = x^ρ exp (-Q (x)), where ρ > - 1/2 and Q is continuous and increasing on I, with limit ∞ at d. We study the orthonormal polynomials associated with the weight W_ρ², obtaining bounds on the orthonormal polynomials, zeros, and Christoffel functions. In addition, we obtain restricted range inequalities.