Legendre polynomials
System of complete and orthogonal polynomials / From Wikipedia, the free encyclopedia
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For Legendre's Homogeneous equation, see Legendre's equation.
Not to be confused with Lagrange polynomial (the interpolating polynomial).
In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast 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 functions, Legendre functions of the second kind, big q-Legendre polynomials, and associated Legendre functions.