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...

(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...

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

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...

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

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 (...

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

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...

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

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

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

referred to as Brewer polynomials. Over the complex numbers, Dickson polynomials are essentially equivalent to Chebyshev polynomials with a change of variable...

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

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...

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...

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

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

\cos(nx)} is a polynomial of cos ⁡ x , {\displaystyle \cos x,} the so-called Chebyshev polynomial of the first kind, see Chebyshev polynomials#Trigonometric...

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

Laguerre polynomials Chebyshev polynomials Legendre polynomials Jacobi polynomials Others come from statistics: Hermite polynomials Many are studied in...

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...

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