Polynomials satisfying a certain twin asymptotic periodic recurrence relation are considered. It is assumed that the coefficients of the recurrence formula are unbounded but vary regularly and have different behaviour for even and odd indices. The asymptotic behaviour of the ratio of contiguous polynomials is analyzed.
"Asymptotics for Polynomials Satisfying a Certain Twin Asymptotic Periodic Recurrence Relation: Unbounded Cases." Methods Appl. Anal. 14 (1) 29 - 44, March 2007.