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)}...

analysis, Chebyshev nodes (also called Chebyshev points or a Chebyshev grid) are a set of specific algebraic numbers used as nodes for polynomial interpolation...

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

the Chebyshev inequality (which can be used to prove the weak law of large numbers), the Bertrand–Chebyshev theorem, Chebyshev polynomials, Chebyshev linkage...

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

(1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold Gegenbauer...

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...

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

equation and the Chebyshev polynomials: If T i ( x ) {\displaystyle T_{i}(x)} and U i ( x ) {\displaystyle U_{i}(x)} are the Chebyshev polynomials of the first...

"quadrature", that are based on an expansion of the integrand in terms of Chebyshev polynomials. Equivalently, they employ a change of variables x = cos ⁡ θ {\displaystyle...

summation, is a recursive method to evaluate a linear combination of Chebyshev polynomials. The method was published by Charles William Clenshaw in 1955. It...

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

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

(including as a special case the Gegenbauer polynomials, Chebyshev polynomials, and Legendre polynomials). They have many important applications in such...

Gegenbauer polynomials, and thus also the Legendre, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials. The Jacobi polynomials were...

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...

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

two polynomials are Ψ 1 ( x ) = x − 2 {\displaystyle \Psi _{1}(x)=x-2} and Ψ 2 ( x ) = x + 2. {\displaystyle \Psi _{2}(x)=x+2.} The polynomials Ψ n (...

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

polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials. The original use of interpolation polynomials was...

a similar way from the Lucas numbers are called Lucas polynomials. These Fibonacci polynomials are defined by a recurrence relation: F n ( x ) = { 0 ...

Zolotarev polynomials are polynomials used in approximation theory. They are sometimes used as an alternative to the Chebyshev polynomials where accuracy...

Chebyshev may refer to: Pafnuty Chebyshev: A Russian mathematician Chebyshev function: Number-theory functions Chebyshev polynomials Chebyshev filter Chebyshev's...

2 {\displaystyle \delta ={\frac {N-1}{N}}{\frac {\pi }{2}}} are Chebyshev polynomials of the first kind of degree N. This property is exploited to produce...

{\pi }{n+1}}\sin ^{2}\left({\frac {i}{n+1}}\pi \right).\,} Chebyshev polynomials Chebyshev nodes Abramowitz, M & Stegun, I A, Handbook of Mathematical...

where Tn(x) is a Chebyshev polynomial of the first kind. Many properties can be derived from the properties of the Chebyshev polynomials of the first kind...

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

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

the ring is a finite field, the Dickson polynomials, which are closely related to the Chebyshev polynomials, provide examples. Over a finite field, every...

Chebyshev function in number theory Chebyshev integral Chebyshev iteration Chebyshev method Chebyshev nodes Chebyshev polynomials and the "Chebyshev form"...