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

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

In mathematics, discrete Chebyshev polynomials, or Gram polynomials, are a type of discrete orthogonal polynomials used in approximation theory, introduced...

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

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

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

In mathematics, Gottlieb polynomials are a family of discrete orthogonal polynomials given by ℓ n ( x , λ ) = e − n λ ∑ k ( 1 − e λ ) k ( n k ) ( x k...

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

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)}...

such as the Kravchuk polynomials (Atakishiyev and Wolf, 1997). The "best" choice of eigenvectors to define a fractional discrete Fourier transform remains...

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

partitions, and is closely related to q-series, special functions and orthogonal polynomials. Originally a part of number theory and analysis, partition theory...

A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform...

mathematics, the Al-Salam–Chihara polynomials Qn(x;a,b;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced...

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

random variable in terms of a polynomial function of other random variables. The polynomials are chosen to be orthogonal with respect to the joint probability...

Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves. A numerically stable way to evaluate polynomials in...

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

Chebyshev polynomials, and fast DCT algorithms (below) are used in Chebyshev approximation of arbitrary functions by series of Chebyshev polynomials, for example...

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

Chihara–Ismail polynomials are a family of orthogonal polynomials introduced by Chihara and Ismail (1982), generalizing the van Doorn polynomials introduced...

mathematics, the discrete q-Hermite polynomials are two closely related families hn(x;q) and ĥn(x;q) of basic hypergeometric orthogonal polynomials in the basic...

mean Classical orthogonal polynomials Hermite polynomials Laguerre polynomials Jacobi polynomials Gegenbauer polynomials Legendre polynomials Euclidean space...

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

differintegral Generalized Fourier series Orthogonal functions Orthogonal polynomials Empirical orthogonal functions Set of uniqueness Continuous Fourier...

partitions, and is closely related to q-series, special functions and orthogonal polynomials. Originally a part of number theory and analysis, it is now considered...

Meixner polynomials, are a family of discrete orthogonal polynomials introduced by Josef Meixner Meixner–Pollaczek polynomials, are a family of orthogonal polynomials...

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

also investigated orthogonal polynomials (see Laguerre polynomials). Laguerre's method is a root-finding algorithm tailored to polynomials. He laid the foundations...