Differential equations associated with Legendre polynomials

TL;DR

This paper explores non-linear differential equations related to Legendre polynomials, deriving new identities and discussing their applications in mathematical analysis.

Contribution

It introduces new explicit identities for Legendre polynomials through the study of associated non-linear differential equations.

Findings

Derived new identities for Legendre polynomials

Analyzed applications of these differential equations

Enhanced understanding of polynomial properties

Abstract

In this paper, we study non-linear differential equations associated with Legendre polynomials and their applications. From our study of non- linear differential equations, we derive some new and explicit identities for Legendre polynomials.