mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other...
15 KB (2,079 words) - 21:55, 22 May 2025
classical orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including...
35 KB (6,139 words) - 08:45, 3 February 2025
In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike...
42 KB (6,470 words) - 10:18, 27 May 2025
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets...
67 KB (12,144 words) - 07:49, 5 April 2025
mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of...
38 KB (7,177 words) - 21:53, 22 April 2025
polynomials, Hermite-Padé polynomials or polyorthogonal polynomials. MOPs should not be confused with multivariate orthogonal polynomials. Consider a multiindex...
3 KB (649 words) - 11:59, 27 June 2023
The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}...
58 KB (10,713 words) - 13:33, 7 April 2025
mathematics, a sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with respect to a discrete measure...
2 KB (278 words) - 16:07, 26 June 2024
Legendre polynomials. Another collection of orthogonal polynomials are the associated Legendre polynomials. The study of orthogonal polynomials involves...
6 KB (771 words) - 05:51, 24 December 2024
well-approximated by polynomials on [ − 1 , 1 ] {\displaystyle [-1,1]} , the associated orthogonal polynomials are Legendre polynomials, denoted by Pn(x)...
42 KB (6,792 words) - 01:05, 26 May 2025
{L}}_{k}(x){\mathcal {L}}_{n-k}(y)} Orthogonal polynomials Rodrigues' formula Angelescu polynomials Bessel polynomials Denisyuk polynomials Transverse mode, an important...
34 KB (6,005 words) - 11:01, 2 April 2025
In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P n ( α , β ) ( x ) {\displaystyle P_{n}^{(\alpha ,\beta )}(x)} are...
12 KB (2,449 words) - 13:26, 26 April 2025
Various polynomial sequences named for mathematicians of the past are sequences of orthogonal polynomials. In particular: The Hermite polynomials are orthogonal...
14 KB (2,185 words) - 16:59, 3 May 2025
orthogonal subset of a more general family of little-known Routh polynomials introduced by Edward John Routh in 1884. The term Romanovski polynomials...
19 KB (1,982 words) - 19:13, 31 March 2025
In mathematics, Sobolev orthogonal polynomials are orthogonal polynomials with respect to a Sobolev inner product, i.e. an inner product with derivatives...
3 KB (418 words) - 22:30, 20 March 2024
In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(α) n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight...
9 KB (1,830 words) - 04:33, 12 May 2025
solutions are sometimes called "associated Legendre polynomials", even though they are not polynomials when m is odd. The fully general class of functions...
33 KB (5,915 words) - 11:11, 25 April 2025
families of sieved orthogonal polynomials that have been studied include sieved Pollaczek polynomials, and sieved Jacobi polynomials. Al-Salam, Waleed;...
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many other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials and Askey–Wilson polynomials, which in turn include...
21 KB (3,160 words) - 01:24, 13 September 2024
to fitting m data points by a simple polynomial in the subsidiary variable, z, is to use orthogonal polynomials. Y = b 0 P 0 ( z ) + b 1 P 1 ( z ) ⋯ +...
54 KB (8,147 words) - 21:57, 28 April 2025
elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible...
20 KB (3,773 words) - 12:22, 22 April 2025
In mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle...
7 KB (1,095 words) - 22:15, 19 April 2025
Askey scheme (redirect from Hypergeometric orthogonal polynomials)
organizing orthogonal polynomials of hypergeometric or basic hypergeometric type into a hierarchy. For the classical orthogonal polynomials discussed in...
8 KB (799 words) - 03:53, 27 May 2025
secondary polynomials into an orthogonal system. (For more details see the article secondary measure.) Orthogonal polynomials Secondary polynomials Secondary...
3 KB (527 words) - 17:34, 1 January 2025
circumstances, one can give that space a basis of orthogonal polynomials, the Bergman polynomials. In this case, the analog of the tridiagonal Jacobi...
5 KB (791 words) - 03:45, 30 November 2024
List of q-analogs (section Orthogonal polynomials)
q-Charlier polynomials q-Hahn polynomials q-Jacobi polynomials: Big q-Jacobi polynomials Continuous q-Jacobi polynomials Little q-Jacobi polynomials q-Krawtchouk...
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families of functions are used to form an orthogonal basis, such as in the contexts of orthogonal polynomials, orthogonal functions, and combinatorics. In optics...
16 KB (2,695 words) - 18:06, 20 May 2025
In mathematics, the Bessel polynomials are an orthogonal sequence of polynomials. There are a number of different but closely related definitions. The...
13 KB (2,921 words) - 14:07, 1 February 2025
Newton polynomial Orthogonal polynomials Orthogonal polynomials on the unit circle Permutation polynomial Racah polynomials Rogers polynomials Rogers–Szegő...
5 KB (441 words) - 01:35, 1 December 2023
Rodrigues' formula (category Orthogonal polynomials)
it. The term is also used to describe similar formulas for other orthogonal polynomials. Askey (2005) describes the history of the Rodrigues formula in...
16 KB (3,535 words) - 19:15, 17 March 2025