Monotone Jacobi parameters and non-Szegő weights

We relate asymptotics of Jacobi parameters to asymptotics of the spectral weights near the edges. Typical of our results is that for an≡1an≡1, bn=−Cn−βbn=−Cn−β (0<β<23), one has dμ(x)=w(x)dx on (−2,2)(−2,2), and near x=2x=2, w(x)=e−2Q(x) where Q(x)=β−1C1βΓ(32)Γ(1β−12)(2−x)12−1βΓ(1β+1)(1+O((2−x))).