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There is a page named "Chebyshev polynomial of the first kind" on Wikipedia
several equivalent ways, one of which starts with trigonometric functions: The Chebyshev polynomials of the first kind T n {\displaystyle T_{n}} are...61 KB (11,466 words) - 18:05, 14 August 2024
the Chebyshev zeros, are the zeros of the Chebyshev polynomials of the first kind. The Chebyshev nodes of the second kind, also called the Chebyshev extrema...8 KB (1,201 words) - 19:37, 2 August 2024- the grid of Chebyshev extrema, the extrema of the Chebyshev polynomials of the first kind, which are also the zeros of the Chebyshev polynomials of the...5 KB (960 words) - 16:10, 21 May 2024
{N-1}{N}}{\frac {\pi }{2}}} are Chebyshev polynomials of the first kind of degree N. This property is exploited to produce a set of points, called Padua points...16 KB (1,651 words) - 21:58, 27 November 2023
n}(x)+{\frac {\nu +1}{n}}b_{\nu +1,n}(x).} The expansion of the Chebyshev Polynomials of the First Kind into the Bernstein basis is T n ( u ) = ( 2 n − 1...21 KB (3,797 words) - 00:15, 3 January 2024- to take on any value. The Chebyshev polynomials of the first kind are a special case of Zolotarev polynomials. These polynomials were introduced by Russian...9 KB (1,559 words) - 00:01, 23 May 2024
is a Chebyshev polynomial of the first kind. Many properties can be derived from the properties of the Chebyshev polynomials of the first kind. Other...4 KB (688 words) - 03:13, 27 February 2023- is a polynomial of degree p and it is proportional to the Chebyshev polynomial of the first kind T p ( x ) = ( − 1 ) p / 2 F ( x ) {\displaystyle T_{p}(x)=(-1)^{p/2}\...2 KB (444 words) - 12:25, 7 August 2022
Window function (redirect from List of window functions)k}{N+1}}\right){\big )}}{10^{\alpha }}},\ 0\leq k\leq N.} Tn(x) is the n-th Chebyshev polynomial of the first kind evaluated in x, which can be computed using T n ( x...73 KB (8,651 words) - 20:46, 29 July 2024- Chebyshev in 1859. Chebyshev's work was overlooked, and they were named later after Charles Hermite, who wrote on the polynomials in 1864, describing...57 KB (10,024 words) - 18:31, 4 August 2024
- to Chebyshev polynomials with a change of variable, and, in fact, Dickson polynomials are sometimes called Chebyshev polynomials. Dickson polynomials are...13 KB (2,070 words) - 09:24, 5 July 2023
the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, big q-Legendre polynomials,...31 KB (5,373 words) - 23:47, 14 August 2024- Markov brothers' inequality (section The statement)(2k-1)}}\max _{-1\leq x\leq 1}|P(x)|.} Equality is attained for Chebyshev polynomials of the first kind. Bernstein's inequality (mathematical analysis) Remez inequality...2 KB (282 words) - 04:07, 11 August 2024
- analysis, the Clenshaw algorithm, also called Clenshaw summation, is a recursive method to evaluate a linear combination of Chebyshev polynomials. The method...10 KB (2,169 words) - 13:05, 19 August 2024
Fourier transform (redirect from List of Fourier transforms)the set of homogeneous harmonic polynomials of degree k on Rn be denoted by Ak. The set Ak consists of the solid spherical harmonics of degree k. The...177 KB (21,044 words) - 13:14, 5 August 2024
\cos(nx)} is a polynomial of cos x , {\displaystyle \cos x,} the so-called Chebyshev polynomial of the first kind, see Chebyshev polynomials#Trigonometric...81 KB (12,166 words) - 04:35, 2 August 2024
The Chebyshev polynomials of the first kind are orthogonal with respect to the measure 1 1 − x 2 . {\textstyle {\frac {1}{\sqrt {1-x^{2}}}}.} The Chebyshev...13 KB (2,164 words) - 00:04, 7 May 2024- Rietveld refinement (category Pages that use a deprecated format of the math tags)appear as follows. Again, background is treated as a Chebyshev polynomial of the first kind ("Handbook of Mathematical Functions", M. Abramowitz and IA. Stegun...29 KB (4,968 words) - 22:14, 8 July 2024
- Zeitlin established the following relation between Ψ n ( x ) {\displaystyle \Psi _{n}(x)} and Chebyshev polynomials of the first kind. If n = 2 s + 1 {\displaystyle...10 KB (2,520 words) - 05:05, 23 February 2024
- the data rather than fixed in advance. Discrete Chebyshev transforms (on the 'roots' grid and the 'extrema' grid of the Chebyshev polynomials of the first...7 KB (933 words) - 23:28, 7 November 2023
- Encyclopedia of Mathematics Education (2001) p. 235. It is customary to consider Chebyshev, Gauss, Jacobi, and Legendre as the main creators of the theory of orthogonal
- Chebyshev polynomials of the first kind, denoted Tn and are closely related to cos {\displaystyle \cos } and Chebyshev polynomials of the second kind