Editing Legendre function (section)

{{Short description|Solutions of Legendre's differential equation}}
{{For|the most common case of integer degree|Legendre polynomials|associated Legendre polynomials}}
{{more footnotes|date=January 2013}}

In physical science and mathematics, the '''Legendre functions''' {{math|''P''<sub>''λ''</sub>}}, {{math|''Q''<sub>''λ''</sub>}} and '''associated Legendre functions''' {{math|''P''{{su|p=''μ''|b=''λ''}}}}, {{math|''Q''{{su|p=''μ''|b=''λ''}}}}, and '''Legendre functions of the second kind''', {{math|''Q<sub>n</sub>''}}, 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.

[[File:Associated Legendre Poly.svg|thumb|500px|Associated Legendre polynomial curves for {{math|1=''λ'' = ''l'' = 5}}.]]