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Chebyshev polynomials

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)} and U n ( x ) {\displaystyle U_{n}(x)} . They can be defined in several equivalent ways, one of which starts with trigonometric functions:

Art, Properties & As a basis set

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Overview

Definitions

Relations between the two kinds of Chebyshev polynomials

Explicit expressions

Properties

Examples

  • OEIS On-Line Encyclopedia of Integer Sequences

As a basis set

Families of polynomials related to Chebyshev polynomials

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Chebyshev polynomials

Nodes120
Edges119
Triples142
Avg. degree1.98
Density0.016667
Components1

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Chebyshev polynomials

Top relations

related to Sources · 40
Chebyshev polynomials → Arthur, Bateman, Bateman Manuscript Project, Caltech, Ch, Chapman, Dover, FL, Hall/CRC, Handbook, Handscomb, Harry, Higher Transcendental Functions, Hochstrasser, In Abramowitz, In Erdélyi, Irene, ISBN, Krieger, LCCN
related to External links · 28
Chebyshev polynomials → Advanced Numerical Analysis, Archived, August, Boost, CA, California State University, Chebyshev, Course, Department, Eric, Fullerton, Is, John, Math, Math Overflow, Mathematics, Mathews, MathWorld, May, Media
related to Roots and extrema · 11
Chebyshev polynomials → Both, Chebyshev, Minimal, One, Shabat, Similarly, Specifically, The, They, Thus, Using
related to As a basis set · 8
Chebyshev polynomials → Chebyshev, Fourier, Furthermore, In, Since, Sobolev, These, This
related to Chebyshev polynomials as special cases of more general polynomial families · 6
Chebyshev polynomials → Chebyshev, Dickson, Gegenbauer, In, Jacobi, The Chebyshev
related to Products of Chebyshev polynomials · 6
Chebyshev polynomials → Chebyshev, For, The, The Chebyshev, They, Three
related to Even order modified Chebyshev polynomials · 5
Chebyshev polynomials → Chebyshev, Even, However, Some, Such
related to Generating functions · 5
Chebyshev polynomials → Bigl, Bigr, Chebyshev, The, There
related to Irreducible Factorization of Chebyshev Polynomials · 5
Chebyshev polynomials → Chebyshev, Given, It, Vieta-Fibonacci, Vieta-Lucas
related to Polynomial in Chebyshev form · 5
Chebyshev polynomials → An, Chebyshev, Clenshaw, Polynomials, Such

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Important terminology

displaystyle polynomials chebyshev frac -1 cos begin end polynomial sum left right n-1 kind aligned first even bigl bigr tfrac

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Chebyshev polynomialsrelated to As a basis setIn0.60section
Chebyshev polynomialsrelated to As a basis setSobolev0.60section
Chebyshev polynomialsrelated to As a basis setChebyshev0.60section
Chebyshev polynomialsrelated to As a basis setFurthermore0.60section
Chebyshev polynomialsrelated to As a basis setThis0.60section
Chebyshev polynomialsrelated to As a basis setSince0.60section
Chebyshev polynomialsrelated to As a basis setFourier0.60section
Chebyshev polynomialsrelated to As a basis setThese0.60section
Chebyshev polynomialsrelated to Chebyshev polynomials as special cases of more general polynomial familiesThe Chebyshev0.60section
Chebyshev polynomialsrelated to Chebyshev polynomials as special cases of more general polynomial familiesGegenbauer0.60section
Chebyshev polynomialsrelated to Chebyshev polynomials as special cases of more general polynomial familiesJacobi0.60section
Chebyshev polynomialsrelated to Chebyshev polynomials as special cases of more general polynomial familiesChebyshev0.60section

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