Legendre's differential equation

Named after French mathematician Adrien-Marie Legendre (1752–1833).

Legendre's differential equation

1. (mathematics) The equation that defines the Legendre polynomials: ${\displaystyle {d \over dx}\left[(1-x^{2}){d \over dx}P_{n}(x)\right]+n(n+1)P_{n}(x)=0.}$