Systems of orthogonal polynomials defined by hypergeometric type equations

TL;DR

This paper provides a unified framework for systems of orthogonal polynomials defined by hypergeometric type equations, including their special functions and operators, extending known results to broader classes.

Contribution

It introduces a comprehensive formalism that explicitly characterizes all such polynomial systems and their associated functions and operators, broadening the scope of existing theories.

Findings

Explicit classification of orthogonal polynomial systems

Unified description of associated special functions

Extension of known results to larger function classes

Abstract

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated special functions and the corresponding raising/lowering operators. This general formalism allows us to extend some known results to a larger class of functions.