Asymptotic behavior of orthogonal polynomials. Singular critical case

Our goal is to find an asymptotic behavior as n ? ? of the orthogonal polynomials P ( z ) defined by Jacobi recurrence coefficients a (off-diagonal terms) and b (diagonal terms). We consider case , in such way that ? ? 1 < (that is, Carleman condition violated) ? : = 2 ? . In | ? formulas for are known; they depend crucially on sign study critical The obtained qualitatively different cases 0 + Another paper advocate approach based close analogy difference equations differential Schrödinger type.