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- Chebyshev_polynomials abstract "In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively. One usually distinguishes between Chebyshev polynomials of the first kind which are denoted Tn and Chebyshev polynomials of the second kind which are denoted Un. The letter T is used because of the alternative transliterations of the name Chebyshev as Tchebycheff, Tchebyshev (French) or Tschebyschow (German).The Chebyshev polynomials Tn or Un are polynomials of degree n and the sequence of Chebyshev polynomials of either kind composes a polynomial sequence.Chebyshev polynomials are polynomials with the largest possible leading coefficient, but subject to the condition that their absolute value is bounded on the interval by 1. They are also the extremal polynomials for many other properties.Chebyshev polynomials are important in approximation theory because the roots of the Chebyshev polynomials of the first kind, which are also called Chebyshev nodes, are used as nodes in polynomial interpolation. The resulting interpolation polynomial minimizes the problem of Runge's phenomenon and provides an approximation that is close to the polynomial of best approximation to a continuous function under the maximum norm. This approximation leads directly to the method of Clenshaw–Curtis quadrature.In the study of differential equations they arise as the solution to the Chebyshev differential equationsandfor the polynomials of the first and second kind, respectively. These equations are special cases of the Sturm–Liouville differential equation.".
- Chebyshev_polynomials wikiPageExternalLink download.php?file=%2FPEM%2FPEM2_38_02%2FS001309150001912Xa.pdf&code=c12b9a2fc1aba9e27005a5003ed21b36.
- Chebyshev_polynomials wikiPageExternalLink ChebyshevPolyMod.html.
- Chebyshev_polynomials wikiPageExternalLink is-there-an-intuitive-explanation-for-an-extremal-property-of-chebyshev-polynomia.
- Chebyshev_polynomials wikiPageExternalLink Chebyshev.html.
- Chebyshev_polynomials wikiPageExternalLink lempert.pdf.
- Chebyshev_polynomials wikiPageExternalLink remeztrans.pdf.
- Chebyshev_polynomials wikiPageExternalLink chebfun.
- Chebyshev_polynomials wikiPageID "184539".
- Chebyshev_polynomials wikiPageRevisionID "606577652".
- Chebyshev_polynomials first "P.K.".
- Chebyshev_polynomials first "René F.".
- Chebyshev_polynomials first "Roderick S. C.".
- Chebyshev_polynomials first "Roelof".
- Chebyshev_polynomials first "Tom H.".
- Chebyshev_polynomials hasPhotoCollection Chebyshev_polynomials.
- Chebyshev_polynomials id "18".
- Chebyshev_polynomials id "C/c021940".
- Chebyshev_polynomials last "Koekoek".
- Chebyshev_polynomials last "Koornwinder".
- Chebyshev_polynomials last "Suetin".
- Chebyshev_polynomials last "Swarttouw".
- Chebyshev_polynomials last "Wong".
- Chebyshev_polynomials title "Chebyshev Polynomial of the First Kind".
- Chebyshev_polynomials title "Orthogonal Polynomials".
- Chebyshev_polynomials urlname "ChebyshevPolynomialoftheFirstKind".
- Chebyshev_polynomials subject Category:Approximation_theory.
- Chebyshev_polynomials subject Category:Numerical_analysis.
- Chebyshev_polynomials subject Category:Orthogonal_polynomials.
- Chebyshev_polynomials subject Category:Special_hypergeometric_functions.
- Chebyshev_polynomials type Abstraction100002137.
- Chebyshev_polynomials type Function113783816.
- Chebyshev_polynomials type MathematicalRelation113783581.
- Chebyshev_polynomials type OrthogonalPolynomials.
- Chebyshev_polynomials type Polynomial105861855.
- Chebyshev_polynomials type Relation100031921.
- Chebyshev_polynomials type SpecialHypergeometricFunctions.
- Chebyshev_polynomials comment "In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively. One usually distinguishes between Chebyshev polynomials of the first kind which are denoted Tn and Chebyshev polynomials of the second kind which are denoted Un.".
- Chebyshev_polynomials label "Chebyshev polynomials".
- Chebyshev_polynomials label "Chebyshev-polynoom".
- Chebyshev_polynomials label "Polinomio di Čebyšëv".
- Chebyshev_polynomials label "Polinomios de Chebyshov".
- Chebyshev_polynomials label "Polinômios de Tchebychev".
- Chebyshev_polynomials label "Polynôme de Tchebychev".
- Chebyshev_polynomials label "Tschebyschow-Polynom".
- Chebyshev_polynomials label "Wielomiany Czebyszewa".
- Chebyshev_polynomials label "Многочлены Чебышёва".
- Chebyshev_polynomials label "متعددات الحدود لشيبيشيف".
- Chebyshev_polynomials label "チェビシェフ多項式".
- Chebyshev_polynomials label "切比雪夫多项式".
- Chebyshev_polynomials sameAs Tschebyschow-Polynom.
- Chebyshev_polynomials sameAs Polinomios_de_Chebyshov.
- Chebyshev_polynomials sameAs Polynôme_de_Tchebychev.
- Chebyshev_polynomials sameAs Polinomio_di_Čebyšëv.
- Chebyshev_polynomials sameAs チェビシェフ多項式.
- Chebyshev_polynomials sameAs 체비쇼프_다항식.
- Chebyshev_polynomials sameAs Chebyshev-polynoom.
- Chebyshev_polynomials sameAs Wielomiany_Czebyszewa.
- Chebyshev_polynomials sameAs Polinômios_de_Tchebychev.
- Chebyshev_polynomials sameAs m.0196lx.
- Chebyshev_polynomials sameAs Q619511.
- Chebyshev_polynomials sameAs Q619511.
- Chebyshev_polynomials sameAs Chebyshev_polynomials.
- Chebyshev_polynomials wasDerivedFrom Chebyshev_polynomials?oldid=606577652.
- Chebyshev_polynomials isPrimaryTopicOf Chebyshev_polynomials.