Orthonormal polynomials with generalized Freud-type weights. (Q1874473)

The authors study polynomials, orthonormal with respect to a generalized Freud-type weight \(W_{rQ}^2(x)=| x| ^{2r}\exp(-2Q(x)),\) where \(r>-1/2\) and \(\exp(-2Q(x))\) is a Freud weight. They prove infinite-finite range inequalities, estimates of Christoffel functions, the largest zeros and spacing of zeros for those orthonormal polynomials. The results extend and improve corresponding results for other classes of weights [see \textit{E.Levin} and \textit{D. S. Lubinsky}, ``Orthogonal polynomials for exponential weights'' (2001; Zbl 0997.42011)].