An Etymological Dictionary of Astronomy and Astrophysics

The → differential equation of the form: d/dx(1 - x²)dy/dx) + n(n + 1)y = 0. The general solution of the Legendre equation is given by y = c₁P_n(x) + c₂Q_n(x), where P_n(x) are Legendre polynomials and Q_n(x) are called Legendre functions of the second kind.

See also: Named after Adrien-Marie Legendre (1752-1833),
a French mathematician who made important contributions to statistics, number theory, abstract algebra, and mathematical analysis; → equation.