In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation ( 1 − x 2 ) d 2 d x 2 P ℓ m ( x ) − 2...

the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, big q-Legendre polynomials, and...

Qn, are all solutions of Legendre's differential equation. The Legendre polynomials and the associated Legendre polynomials are also solutions of the...

mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him. He is also known for his...

mathematician Associated Legendre polynomials Legendre's equation Legendre polynomials Legendre symbol Legendre transformation Legendre (crater), a lunar impact...

(including as a special case the Gegenbauer polynomials, Chebyshev polynomials, and Legendre polynomials). They have many important applications in such...

left-hand side is played by the Legendre polynomials. The addition theorem states where Pℓ is the Legendre polynomial of degree ℓ. This expression is...

Legendre polynomials Associated Legendre polynomials Spherical harmonic Lucas polynomials Macdonald polynomials Meixner polynomials Necklace polynomial Newton...

the Legendre polynomials. Another collection of orthogonal polynomials are the associated Legendre polynomials. The study of orthogonal polynomials involves...

function of latitude and may be expressed as an infinite sum of associated Legendre polynomials; the functions are orthogonal over the sphere in the continuous...