A system of polynomial s that are mutually orthogonal ( orthogonality is the higher-dimensional analog of perpendicularity), useful in solving differential equation s arising in physics and engineering.
The study of such systems began with Adrien-Marie Legendre (1752–1833), who employed a system now known as Legendre polynomials in the solution of problems in celestial mechanics . Other famous examples are the sets of Hermite and Chebyshev polynomials.