# Orthogonal Polynomials related to g-fractions with missing terms

## TL;DR

This paper explores structural and qualitative properties of perturbed g-fractions, introducing gap g-fractions and analyzing their relation to hypergeometric functions and Pick functions.

## Contribution

It introduces the concept of gap g-fractions and investigates their properties under different perturbations of g-parameters.

## Key findings

- Introduction of gap g-fractions concept
- Analysis of perturbations using tail sequences and Schur fractions
- Identification of some Pick functions within the class

## Abstract

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 \emph{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 are 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.