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...

polynomials (occasionally called hypergeometric polynomials) P n ( α , β ) ( x ) {\displaystyle P_{n}^{(\alpha ,\beta )}(x)} are a class of classical...

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

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

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

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

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

Zeros ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials". dlmf.nist.gov. "DLMF: §18.18 Sums ‣ Classical Orthogonal Polynomials ‣ Chapter...

Sobolev orthogonal polynomials in general no longer share some of the nice features that classical orthogonal polynomials have. Sobolev orthogonal polynomials...

include limiting cases of these polynomials, in which case it also includes the classical orthogonal polynomials. Hahn polynomials are defined in terms of generalized...

for two other sets of orthogonal polynomials. In some contrast to the standard classical orthogonal polynomials, the polynomials under consideration differ...

mathematics, the continuous q-Legendre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.Koekoek, Lesky...

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

mathematics, the continuous q-Hermite polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek...

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

Legendre polynomials as the index tends to infinity, near the edges of the support of the weight. There are generalizations to other classical orthogonal polynomials...

In mathematics, Meixner polynomials (also called discrete Laguerre polynomials) are a family of discrete orthogonal polynomials introduced by Josef Meixner (1934)...

Quasi-arithmetic mean Classical orthogonal polynomials Hermite polynomials Laguerre polynomials Jacobi polynomials Gegenbauer polynomials Legendre polynomials Euclidean...

big q-Jacobi polynomials Pn(x;a,b,c;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. The polynomials are given in...

polynomials or Krawtchouk polynomials (also written using several other transliterations of the Ukrainian surname Кравчу́к) are discrete orthogonal polynomials...

Hermite polynomials Hermite polynomials, a sequence of polynomials orthogonal with respect to the normal distribution Continuous q-Hermite polynomials Continuous...

In mathematics, the q-Meixner polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter...

Q-Hermite Polynomials and Classical Orthogonal Polynomials, arXiv:math/9405213 Al-Salam, W. A.; Carlitz, L. (1965), "Some orthogonal q-polynomials", Mathematische...

In mathematics, the q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme Roelof Koekoek, Peter...

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

theory of orthogonal polynomials, Bochner's theorem is a characterization theorem of certain families of orthogonal polynomials as polynomial solutions...

In mathematics, the q-Charlier polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter...

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

continuous q-Jacobi polynomials P(α,β) n(x|q), introduced by Askey & Wilson (1985), are a family of basic hypergeometric orthogonal polynomials in the basic...