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

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.