Discrete orthogonal polynomials
- Discrete orthogonal polynomials
-
In mathematics, a sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with repect to a discrete measure. Examples include the discrete Chebyshev polynomials, Charlier polynomials, Krawtchouk polynomials, Meixner polynomials, dual Hahn polynomials, Hahn polynomials, and Racah polynomials.
If the measure has finite support, then the corresponding sequence of discrete orthogonal polynomials has only a finite number of elements. The Racah polynomials give an example of this.
References
- Baik, Jinho; Kriecherbauer, T.; McLaughlin, K. T.-R.; Miller, P. D. (2007), Discrete orthogonal polynomials. Asymptotics and applications, Annals of Mathematics Studies, 164, Princeton University Press, ISBN 978-0-691-12734-7; 978-0-691-12734-7, MR2283089, http://books.google.com/books?id=S-GIGgx05kgC
Wikimedia Foundation.
2010.
Look at other dictionaries:
Discrete Chebyshev polynomials — Not to be confused with Chebyshev polynomials. In mathematics, discrete Chebyshev polynomials, or Gram polynomials, are a type of discrete orthogonal polynomials used in approximation theory, introduced by Pafnuty Chebyshev (1864) and… … Wikipedia
Orthogonal polynomials — In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the… … Wikipedia
Discrete q-Hermite polynomials — In mathematics, the discrete q Hermite polynomials are two closely related families hn(x;q) and ĥn(x;q) of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Al Salam and Carlitz (1965). Roelof Koekoek,… … Wikipedia
Discrete mathematics — For the mathematics journal, see Discrete Mathematics (journal). Graphs like this are among the objects studied by discrete mathematics, for their interesting mathematical properties, their usefulness as models of real world problems, and their… … Wikipedia
Meixner polynomials — Not to be confused with Meixner–Pollaczek polynomials. In mathematics, Meixner polynomials (also called discrete Laguerre polynomials) are a family of discrete orthogonal polynomials introduced by Josef Meixner (1934). They are given in… … Wikipedia
Discrete cosine transform — A discrete cosine transform (DCT) expresses a sequence of finitely many data points in terms of a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous applications in science and engineering, from lossy… … Wikipedia
Discrete Fourier transform — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms In mathematics, the discrete Fourier transform (DFT) is a specific kind of discrete transform, used in… … Wikipedia
Chebyshev polynomials — Not to be confused with discrete Chebyshev polynomials. In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev,[1] are a sequence of orthogonal polynomials which are related to de Moivre s formula and which can be defined… … Wikipedia
Chihara–Ismail polynomials — In mathematics, the Chihara–Ismail polynomials are a family of orthogonal polynomials introduced by Chihara and Ismail (1982), generalizing the van Doorn polynomials introduced by van Doorn (1981) and the Karlin–McGregor polynomials. They… … Wikipedia
Kravchuk polynomials — or Krawtchouk polynomials are classical orthogonal polynomials associated with the binomial distribution, introduced by the Ukrainian mathematician Mikhail Kravchuk in 1929. [Sur une généralisation des polynomes d Hermite. Note de M.Krawtchouk, C … Wikipedia
