mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other...

classical orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including...

In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike...

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets...

polynomials, Hermite-Padé polynomials or polyorthogonal polynomials. MOPs should not be confused with multivariate orthogonal polynomials. Consider a multiindex...

mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of...

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)}...

mathematics, a sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with respect to a discrete measure...

{L}}_{k}(x){\mathcal {L}}_{n-k}(y)} Orthogonal polynomials Rodrigues' formula Angelescu polynomials Bessel polynomials Denisyuk polynomials Transverse mode, an important...

well-approximated by polynomials on [ − 1 , 1 ] {\displaystyle [-1,1]} , the associated orthogonal polynomials are Legendre polynomials, denoted by Pn(x)...

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

Various polynomial sequences named for mathematicians of the past are sequences of orthogonal polynomials. In particular: The Hermite polynomials are orthogonal...

orthogonal subset of a more general family of little-known Routh polynomials introduced by Edward John Routh in 1884. The term Romanovski polynomials...

In mathematics, Sobolev orthogonal polynomials are orthogonal polynomials with respect to a Sobolev inner product, i.e. an inner product with derivatives...

In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P n ( α , β ) ( x ) {\displaystyle P_{n}^{(\alpha ,\beta )}(x)} are...

solutions are sometimes called "associated Legendre polynomials", even though they are not polynomials when m is odd. The fully general class of functions...

In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(α) n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight...

families of sieved orthogonal polynomials that have been studied include sieved Pollaczek polynomials, and sieved Jacobi polynomials. Al-Salam, Waleed;...

elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible...

many other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials and Askey–Wilson polynomials, which in turn include...

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 ) ⋯ +...

secondary polynomials into an orthogonal system. (For more details see the article secondary measure.) Orthogonal polynomials Secondary polynomials Secondary...

organizing orthogonal polynomials of hypergeometric or basic hypergeometric type into a hierarchy. For the classical orthogonal polynomials discussed in...

circumstances, one can give that space a basis of orthogonal polynomials, the Bergman polynomials. In this case, the analog of the tridiagonal Jacobi...

In mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle...

families of functions are used to form an orthogonal basis, such as in the contexts of orthogonal polynomials, orthogonal functions, and combinatorics. In optics...

In mathematics, the Bessel polynomials are an orthogonal sequence of polynomials. There are a number of different but closely related definitions. The...

generation and made fundamental contributions to the theory of orthogonal polynomials and Toeplitz matrices building on the work of his contemporary Otto...

q-Charlier polynomials q-Hahn polynomials q-Jacobi polynomials: Big q-Jacobi polynomials Continuous q-Jacobi polynomials Little q-Jacobi polynomials q-Krawtchouk...

it. The term is also used to describe similar formulas for other orthogonal polynomials. Askey (2005) describes the history of the Rodrigues formula in...