Associated special functions and coherent states

TL;DR

This paper unifies the theory of orthogonal polynomials, associated special functions, and coherent states derived from hypergeometric type equations, extending known results to broader classes.

Contribution

It provides a comprehensive and explicit framework linking hypergeometric equations to orthogonal polynomials, special functions, and coherent states, generalizing previous specific cases.

Findings

Unified formalism for orthogonal polynomials and special functions

Explicit construction of associated coherent states

Extension of known results to broader 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 some systems of coherent states. This general formalism allows us to extend some results known only in particular cases.