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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.
This entry comes from Encyclopædia Britannica Concise. For the full entry on orthogonal polynomials, visit Britannica.com.
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