Raising and lowering operators and their factorization for generalized orthogonal polynomials of hypergeometric type on homogeneous and non-homogeneous lattice

TL;DR

This paper extends the construction of raising and lowering operators to generalized orthogonal polynomials of hypergeometric type on both homogeneous and non-homogeneous lattices, enhancing the algebraic tools for their analysis.

Contribution

It completes and extends the operators for orthogonal polynomials of hypergeometric type to generalized cases on various lattices.

Findings

Constructed explicit raising and lowering operators for generalized orthogonal polynomials.

Extended the operator framework to non-homogeneous lattices.

Provided a unified approach for hypergeometric-type difference equations.

Abstract

We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal polynomials, namely, those difference of orthogonal polynomials that satisfy a similar difference equation of hypergeometric type.