In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number...
31 KB (5,385 words) - 15:23, 18 April 2024
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...
31 KB (5,475 words) - 23:52, 6 March 2024
mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him. He is also known for his...
17 KB (1,804 words) - 23:42, 10 May 2024
with Gauss–Legendre quadrature, the associated orthogonal polynomials are Legendre polynomials, denoted by Pn(x). With the n-th polynomial normalized...
13 KB (1,597 words) - 04:38, 25 March 2024
Qn, are all solutions of Legendre's differential equation. The Legendre polynomials and the associated Legendre polynomials are also solutions of the...
11 KB (1,723 words) - 11:01, 15 May 2024
Gaussian quadrature (redirect from Gauss legendre quadrature)
well-approximated by polynomials on [ − 1 , 1 ] {\displaystyle [-1,1]} , the associated orthogonal polynomials are Legendre polynomials, denoted by Pn(x)...
42 KB (6,793 words) - 06:22, 1 April 2024
(1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold...
7 KB (1,339 words) - 21:00, 11 July 2023
mathematics, Legendre transform is an integral transform named after the mathematician Adrien-Marie Legendre, which uses Legendre polynomials P n ( x ) {\displaystyle...
4 KB (340 words) - 17:00, 19 July 2022
(including as a special case the Gegenbauer polynomials, Chebyshev polynomials, and Legendre polynomials). They have many important applications in such...
35 KB (6,102 words) - 20:33, 17 November 2022
Gegenbauer polynomials form the most important class of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as special...
14 KB (1,891 words) - 20:13, 17 May 2024