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  2. Chebyshev polynomials - Wikipedia

    en.wikipedia.org/wiki/Chebyshev_polynomials

    Plot of the Chebyshev polynomial of the first kind () with = in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D. The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as () and ().

  3. Chebyshev nodes - Wikipedia

    en.wikipedia.org/wiki/Chebyshev_nodes

    Here we plot the Chebyshev nodes of the first kind and the second kind, both for n = 8. For both kinds of nodes, we first plot the points equi-distant on the upper half unit circle in blue. Then the blue points are projected down to the x-axis. The projected points, in red, are the Chebyshev nodes.

  4. File:Chebyshev Polynomials of the 2nd Kind (n=0-5, x=(-1,1 ...

    en.wikipedia.org/wiki/File:Chebyshev_Polynomials...

    File:Chebyshev Polynomials of the 2nd Kind (n=0-5, x=(-1,1)).svg. Add languages. Page contents not supported in other languages. File; Talk;

  5. Chebyshev equation - Wikipedia

    en.wikipedia.org/wiki/Chebyshev_equation

    Chebyshev's equation is the second order linear differential equation + = where p is a real (or complex) constant. The equation is named after Russian mathematician Pafnuty Chebyshev. The solutions can be obtained by power series:

  6. Orthogonal polynomials - Wikipedia

    en.wikipedia.org/wiki/Orthogonal_polynomials

    The Gegenbauer polynomials form the most important class of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as special cases. The field of orthogonal polynomials developed in the late 19th century from a study of continued fractions by P. L. Chebyshev and was pursued by A. A. Markov and T. J. Stieltjes.

  7. Discrete Chebyshev transform - Wikipedia

    en.wikipedia.org/wiki/Discrete_Chebyshev_transform

    Like the Chebyshev polynomials, it is named after Pafnuty Chebyshev. The two most common types of discrete Chebyshev transforms use the grid of Chebyshev zeros, the zeros of the Chebyshev polynomials of the first kind () and the grid of Chebyshev extrema, the extrema of the Chebyshev polynomials of the first kind, which are also the zeros of ...

  8. Theodore J. Rivlin - Wikipedia

    en.wikipedia.org/wiki/Theodore_J._Rivlin

    For many years he was an associate editor for the Journal of Approximation Theory and wrote over 80 research articles on approximation theory and computational mathematics. [1] The Annals of Numerical Analysis published in 1997 a special issue entitled The Heritage of P.L. Chebyshev: A Festschrift in honor of the 70th birthday of T.J. Rivlin. [4]

  9. Dickson polynomial - Wikipedia

    en.wikipedia.org/wiki/Dickson_polynomial

    The Dickson polynomials with parameter α = 1 are related to Chebyshev polynomials T n (x) = cos (n arccos x) of the first kind by [1] (,) = (). Since the Dickson polynomial D n (x,α) can be defined over rings with additional idempotents, D n (x,α) is often not related to a Chebyshev polynomial.