# On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices

## TL;DR

This paper explores the relationship between classical orthogonal polynomials and Hankel matrices with entries satisfying second order linear recurrences, providing new characterizations of their Cholesky factorizations.

## Contribution

It establishes a novel link between classical moment functionals, orthogonal polynomials, and Hankel matrices through recurrence relations and Cholesky factorization characterizations.

## Key findings

- Characterization of Hankel matrices with recurrent entries
- Link between Cholesky factors and classical orthogonal polynomials
- New insights into the structure of moment functionals

## Abstract

Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second order linear recurrence relation. In this work, we use this characterization to link the theory of classical orthogonal polynomials and the study of Hankel matrices whose entries satisfy a second order linear recurrence relation. Using the recurrent character of the entries of such Hankel matrices, we give several characterizations of the triangular and diagonal matrices involved in their Cholesky factorization and connect them with a corresponding characterization of classical orthogonal polynomials.