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

The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)} and...

include the discrete Chebyshev polynomials, Charlier polynomials, Krawtchouk polynomials, Meixner polynomials, dual Hahn polynomials, Hahn polynomials, and Racah...

Gegenbauer polynomials form the most important class of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as special...

of Chebyshev nodes and coefficients of a function in Chebyshev polynomial basis. Like the Chebyshev polynomials, it is named after Pafnuty Chebyshev. The...

a polynomial of degree N. One can obtain polynomials very close to the optimal one by expanding the given function in terms of Chebyshev polynomials and...

Hermite polynomials were defined by Pierre-Simon Laplace in 1810, though in scarcely recognizable form, and studied in detail by Pafnuty Chebyshev in 1859...

form" Chebyshev norm Discrete Chebyshev polynomials Discrete Chebyshev transform Chebyshev rational functions Chebyshev–Gauss quadrature Chebyshev–Markov–Stieltjes...

named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials. Type I Chebyshev filters are usually referred...

Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials, introduced by Pafnuty Chebyshev in...

multiple dimensions Discrete Chebyshev polynomials — polynomials orthogonal with respect to a discrete measure Favard's theorem — polynomials satisfying suitable...

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

terms of Chebyshev polynomials. Equivalently, they employ a change of variables x = cos ⁡ θ {\displaystyle x=\cos \theta } and use a discrete cosine transform...

4}\delta ^{-2}n^{-1}.} (Chebyshev's inequality) It follows that the polynomials fn tend to f uniformly. Bernstein polynomials can be generalized to k...

{\displaystyle s_{n}} . The polynomials are normalized by setting ω c = 1 {\displaystyle \omega _{c}=1} . The normalized Butterworth polynomials then have the general...

wavelets are examples of orthogonal functions with discrete ranges. Legendre and Chebyshev polynomials provide orthogonal families for the interval [−1...

derived at the Chebyshev Gauss–Lobatto collocation points by using the discrete orthogonal relationship of the Chebyshev polynomials. Then, using two...

mathematics, the dual Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined on...

non-uniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier...

between Shabat polynomials and Chebyshev polynomials, Shabat polynomials themselves are sometimes called generalized Chebyshev polynomials. Different trees...

parameter α sets the Chebyshev norm of the sidelobes to −20α decibels. The window function can be calculated from W0(k) by an inverse discrete Fourier transform...

fast algorithms for discrete cosine or sine transforms (e.g. fast DCT used for JPEG and MPEG/MP3 encoding and decoding), fast Chebyshev approximation, solving...

than fixed in advance. Discrete Chebyshev transforms (on the 'roots' grid and the 'extrema' grid of the Chebyshev polynomials of the first kind). This...

|f(s)|:s\in S\,\right\}.} This norm is also called the supremum norm, the Chebyshev norm, the infinity norm, or, when the supremum is in fact the maximum...

Chebyshev polynomials. Linear interpolation uses a linear function for each of intervals [xk,xk+1]. Spline interpolation uses low-degree polynomials in...

polynomials in r1, r2, r3, and a. The proof then results in the verification of the equality of two polynomials. If the coefficients of a polynomial are...

(LCCD) via the Z-transform. The discrete frequency-domain transfer function is written as the ratio of two polynomials. For example: H ( z ) = ( z + 1...

discrete Chebyshev polynomial, and the corresponding eigenvalue, P ℓ ( cos ⁡ β ) {\displaystyle P_{\ell }(\cos \beta )} , is the Legendre polynomial....

given order Chebyshev filter (Type I) – maximally flat in stopband, sharper cutoff than a Butterworth filter of the same order Chebyshev filter (Type...

Chebyshev space is the subspace of Chebyshev polynomials of order n in the space of real continuous functions on an interval, C[a, b]. The polynomial...