Orthogonal Polynomials Related to g-Fractions with Missing Terms

The purpose of the present paper is to investigate some structural and qualitative aspects of two different perturbations of the parameters of g -fractions. In this context, the concept of gap g -fractions is introduced. While tail sequences of a continued fraction play a significant role in the first perturbation, Schur fractions are used in the second perturbation of the g -parameters that is considered. Illustrations are provided using Gaussian hypergeometric functions. Using a particular gap g -fraction, some members of the class of Pick functions are also identified.