Plancherel-Rotach-type asymptotics for orthogonal polynomials associated with \(\exp (-x^ 6/6)\) (Q1821992)

Consider the weight \(f(x)=\exp (-x^ 6/6)\) on the real line and the associated sequence of orthonormal polynomials. The differential equation satisfied by this sequence is given and then used to find the strong asymptotic behavior of the orthonormal sequence. The solution to this problem for an arbitrary weight of the form \(f(x)-\exp (-x^{\lambda})\), \(\lambda >0\), was announced by \textit{E. A. Rakhmanov} in the Proceedings of the Second Conference of Orthogonal Polynomials and its Applications. Segovia 86 [to appear in Lect. Notes Math. (Springer-Verlag)].