# Orthogonal polynomials on the real line corresponding to a perturbed chain sequence

## TL;DR

This paper investigates how perturbations of chain sequences influence orthogonal polynomials on the real line, revealing connections to measure transformations and illustrating with Laguerre polynomials.

## Contribution

It introduces a specific perturbation of chain sequences affecting orthogonal polynomials on [0,∞) and links these to measure transformations, with applications to Laguerre polynomials.

## Key findings

- Perturbations relate to transformations of symmetric measures.
- The study reveals kernel polynomial consequences of chain sequence disturbances.
- Application to generalized Laguerre polynomials demonstrates the theory.

## Abstract

In recent years, chain sequences and their perturbations have played a significant role in characterising the orthogonal polynomials both on the real line as well as on the unit circle. In this note, a particular disturbance of the chain sequence related to orthogonal polynomials having their true interval of orthogonality as a subset of $[0,\infty)$ is studied leading to an important consequence related to the kernel polynomials. Such perturbations are shown to be related to transformations of symmetric measures. An illustration using the generalized Laguerre polynomials is also provided.