Fr.: équation de Legendre
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 = c1Pn(x) + c2Qn(x), where Pn(x) are Legendre polynomials and Qn(x) are called Legendre functions of the second kind.
Named after Adrien-Marie Legendre (1752-1833), a French mathematician who made important contributions to statistics, number theory, abstract algebra, and mathematical analysis; → equation.