Orthonormal polynomials with exponential-type weights

Let R=(-∞,∞) and let wρ(x)≔|x|ρexp(-Q(x)), where and Q(x)∈C2:R→R+=[0,∞) is an even function. In this paper we consider the properties of the orthonormal polynomials with respect to the weight , obtaining bounds on the orthonormal polynomials and spacing on their zeros. Moreover, we estimate An(x) and Bn(x) defined in Section 4, which are used in representing the derivative of the orthonormal polynomials with respect to the weight .