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In physical science and mathematics, the Legendre functions Pλ, Qλ and associated Legendre functions Pμ
λ, Qμ
λ, and Legendre functions of the second kind, Qn, are all solutions of Legendre's differential equation. The Legendre polynomials and the associated Legendre polynomials are also solutions of the differential equation in special cases, which, by virtue of being polynomials, have a large number of additional properties, mathematical structure, and applications. For these polynomial solutions, see the separate Wikipedia articles.
