orthogonal polynomials

orthogonal polynomials

A system of polynomials that are mutually orthogonal (orthogonality is the higher-dimensional analog of perpendicularity), useful in solving differential equations 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.