On the Meixner-Pollaczek polynomials and the Sturm-Liouville problems

TL;DR

This paper investigates Meixner-Pollaczek polynomials through Sturm-Liouville problems, providing solutions to recursion relations and exploring associated difference equations and second-kind functions.

Contribution

It introduces new solutions to the recursion relations of Meixner-Pollaczek polynomials using difference operators and analyzes their Sturm-Liouville properties.

Findings

Two linearly independent solutions to the recursion relation

Derivation of associated difference equations

Discussion of second-kind functions

Abstract

This work provides a detailed study of Meixner-Pollaczek polynomials and employs the central difference operator to study the Sturm-Liouville problem. It presents two linearly independent solutions to the recursion relation, along with the associated difference equations. Additionally, the establishment of second-kind functions is discussed.