A Note on the Generalized and Universal Associated Legendre Equations

TL;DR

This paper provides explicit hypergeometric solutions to a class of second-order differential equations related to the Generalized and Universal Associated Legendre Equations, facilitating future research in mathematical physics.

Contribution

It establishes the relationship between these differential equations and the Legendre equations and offers explicit solutions to aid further studies.

Findings

Explicit hypergeometric solutions derived

Connection established with Legendre equations

Potential for future applications in physics

Abstract

A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated Legendre Equations are examined and established. The hypergeometric solutions, presented in this work, will promote future investigations of their mathematical properties and applications to problems in theoretical physics.