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 Encyclopedia of Keywords > Mathematics > Algebra > Polynomials > Orthogonal Polynomials > Chebyshev Polynomials Michael Charnine

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### DefinitionsUpDw('Definitions','-Abz-');

1. The Chebyshev polynomials are a special case of the ultraspherical or Gegenbauer polynomials, which themselves are a special case of the Jacobi polynomials.

### Pafnuty ChebyshevUpDw('PAFNUTY_CHEBYSHEV','-Abz-');

1. This type of filter is named in honor of Pafnuty Chebyshev because their mathematical characteristics are derived from Chebyshev polynomials.

### ApproximationsUpDw('APPROXIMATIONS','-Abz-');

1. The GNU Scientific Library calculates values of the standard normal cdf using Hart’s algorithms and approximations with Chebyshev polynomials.

### Orthogonal PolynomialsUpDw('ORTHOGONAL_POLYNOMIALS','-Abz-');

1. The distribution function is expanded in a series of orthogonal polynomials, namely the Chebyshev polynomials.

### ExpansionUpDw('EXPANSION','-Abz-');

1. The same is true if the expansion is in terms of Chebyshev polynomials.

### IntervalUpDw('INTERVAL','-Abz-');

1. Generalizing to any interval [ a, b] is straightforward by scaling the Chebyshev polynomials.

### Numerical AnalysisUpDw('NUMERICAL_ANALYSIS','-Abz-');

1. Far from being an esoteric subject, Chebyshev polynomials lead one on a journey through all areas of numerical analysis.

### PolynomialsUpDw('POLYNOMIALS','-Abz-');

1. The Chebyshev polynomials T n or U n are polynomials of degree n and the sequence of Chebyshev polynomials of either kind composes a polynomial sequence.
2. He examined the zeros of polynomials of best approximation and produced results which were analogues to properties of the Chebyshev polynomials.

### Second KindUpDw('SECOND_KIND','-Abz-');

1. The Chebyshev polynomials of the second kind are orthogonal polynomials with respect to the Wigner semicircle distribution.

### First KindUpDw('FIRST_KIND','-Abz-');

1. Many properties can be derived from the properties of the Chebyshev polynomials of the first kind.

### Chebyshev PolynomialsUpDw('CHEBYSHEV_POLYNOMIALS','-Abz-');

1. An arbitrary polynomial of degree N can be written in terms of the Chebyshev polynomials of the first kind.
2. In this article we use Java applets to interactively explore some of the classical results on approximation using Chebyshev polynomials.

### CategoriesUpDw('Categories','-Abz-');

1. Mathematics > Algebra > Polynomials > Orthogonal Polynomials
2. First Kind
3. Best Approximation
4. Classical Results
5. Second Kind
6. Books about "Chebyshev Polynomials" in Amazon.com
 Short phrases about "Chebyshev Polynomials"   Originally created: April 05, 2008.   Please send us comments and questions by this Online Form   Please click on to move good phrases up.
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