Orthonormal polynomials for generalized Freud-type weights and higher-order Hermite–Fejér interpolation polynomials

AbstractLet Q:R→R be even, nonnegative and continuous, Q′ be continuous, Q′>0 in (0,∞), and let Q″ be continuous in (0,∞). Furthermore, Q satisfies further conditions. We consider a certain generalized Freud-type weight WrQ2(x)=|x|2rexp(−2Q(x)). In previous paper (J. Approx. Theory 121 (2003) 13) we studied the properties of orthonormal polynomials {Pn(WrQ2;x)}n=0∞ with the generalized Freud-type weight WrQ2(x) on R. In this paper we treat three themes. Firstly, we give an estimate of Pn(WrQ2;x) in the Lp-space, 0