Editing Legendre polynomials (section)

{{Short description|System of complete and orthogonal polynomials}}
{{distinguish|text = [[Lagrange polynomial]] (the interpolating polynomial)}}

[[File:Legendrepolynomials6.svg|360px|thumb|The first six Legendre polynomials]]

In [[mathematics]], '''Legendre polynomials''', named after [[Adrien-Marie Legendre]] (1782), are a system of complete and [[orthogonal polynomials]] with a wide number of mathematical properties and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications.

Closely related to the Legendre polynomials are [[associated Legendre polynomials]], [[Legendre function]]s, Legendre functions of the second kind, [[big q-Legendre polynomials]], and [[associated Legendre function]]s.