Search results
Results from the WOW.Com Content Network
File:Chebyshev Polynomials of the 2nd Kind (n=0-5, x=(-1,1)).svg. Add languages. Page contents not supported in other languages. ... Printable version; Page information;
A Chebyshev polynomial of either kind with degree n has n different simple roots, called Chebyshev roots, in the interval [−1, 1]. The roots of the Chebyshev polynomial of the first kind are sometimes called Chebyshev nodes because they are used as nodes in polynomial interpolation.
The Chebyshev nodes of the second kind, also called the Chebyshev extrema, are the extrema of the Chebyshev polynomials of the first kind, which are also the zeros of the Chebyshev polynomials of the second kind. Both of these sets of numbers are commonly referred to as Chebyshev nodes in literature. [1]
You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.
The zeroes of the elliptic rational function will be the zeroes of the polynomial in the numerator of the function. The following derivation of the zeroes of the elliptic rational function is analogous to that of determining the zeroes of the Chebyshev polynomials (Lutovac, Tošić & Evans 2001, § 12.6). Using the fact that for any z
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:
Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory. NY: Wiley. 1990; 249 pages, revised 2nd edition of The Chebyshev Polynomials ; addition of about 80 exercises, a chapter introducing some elementary algebraic and number theoretic properties of the Chebyshev polynomials, and additional coverage of the polynomials ...
In numerical analysis Chebyshev–Gauss quadrature is an extension of Gaussian quadrature method for approximating the value of integrals of the following kind ...