Deformation of the three-term recursion relation and the generation of new orthogonal polynomials

TL;DR

This paper explores how deforming the three-term recursion relation affects orthogonal polynomials, deriving new solutions and density functions related to the deformation parameters.

Contribution

It introduces solutions for a deformed recursion relation and constructs new orthogonal polynomials with associated density functions.

Findings

Derived solutions for deformed recursion relations

Constructed new orthogonal polynomials

Expressed new density functions in terms of original ones

Abstract

We find solutions for a linear deformation of the symmetric three-term recursion relation. The orthogonal polynomials of the first and second kind associated with the deformed relation are obtained. The new density (weight) function is written in terms of the original one and the deformation parameters.