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In mathematics, the Askey–Wilson polynomials (or q-Wilson polynomials) are a family of orthogonal polynomials introduced by Askey and Wilson as q-analogs of the Wilson polynomials. They include many of the other orthogonal polynomials in 1 variable as special or limiting cases, described in the Askey scheme. Askey–Wilson polynomials are the special case of Macdonald polynomials (or Koornwinder polynomials) for the non-reduced affine root system of type (C∨1, C1), and their 4 parameters a, b, c, d correspond to the 4 orbits of roots of this root system. They are defined by

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  • In mathematics, the Askey–Wilson polynomials (or q-Wilson polynomials) are a family of orthogonal polynomials introduced by Askey and Wilson as q-analogs of the Wilson polynomials. They include many of the other orthogonal polynomials in 1 variable as special or limiting cases, described in the Askey scheme. Askey–Wilson polynomials are the special case of Macdonald polynomials (or Koornwinder polynomials) for the non-reduced affine root system of type (C∨1, C1), and their 4 parameters a, b, c, d correspond to the 4 orbits of roots of this root system. They are defined by where φ is a basic hypergeometric function, x = cos θ, and n is the q-Pochhammer symbol. Askey–Wilson functions are a generalization to non-integral values of n. (en)
  • En mathématiques, les polynômes d'Askey-Wilson (ou q-polynômes de Wilson) sont une famille particulière de polynômes orthogonaux. Ils ont été introduits par Richard Askey et James A. Wilson en 1985, et sont nommés d'après eux. Ces polynômes sont des q-analogues d'une autre famille de polynômes orthogonaux, les (en). La famille des polynômes d'Askey-Wilson comprend de nombreux autres polynômes orthogonaux comme cas particuliers, soit en une variable, soit comme cas limite, dans le cadre décrit par le (en). Les polynômes d'Askey-Wilson sont à leur tour des cas particuliers des (en) (ou des (en)) pour certains (en). (fr)
  • Askey–Wilson-polynomen, introducerade av och , är en serie ortogonala polynom och är en av Wilsonpolynomen. De definieras som där x = cos(θ) och n är q-Pochhammersymbolen. (sv)
  • 阿斯基-威尔逊多项式是一个以基本超几何函数表示的正交多项式: 其中阿斯基-威尔逊多项式是威尔逊多项式的q模拟. (zh)
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  • 19582010 (xsd:integer)
dbo:wikiPageLength
  • 3269 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1119091972 (xsd:integer)
dbo:wikiPageWikiLink
dbp:author1Link
  • Richard Askey (en)
dbp:author2Link
  • James A. Wilson (en)
dbp:first
  • René F. (en)
  • Roderick S. C. (en)
  • Roelof (en)
  • Tom H. (en)
dbp:id
  • 18.280000 (xsd:double)
dbp:last
  • Wilson (en)
  • Askey (en)
  • Wong (en)
  • Koekoek (en)
  • Koornwinder (en)
  • Swarttouw (en)
dbp:title
  • Askey-Wilson class (en)
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dbp:year
  • 1985 (xsd:integer)
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rdfs:comment
  • Askey–Wilson-polynomen, introducerade av och , är en serie ortogonala polynom och är en av Wilsonpolynomen. De definieras som där x = cos(θ) och n är q-Pochhammersymbolen. (sv)
  • 阿斯基-威尔逊多项式是一个以基本超几何函数表示的正交多项式: 其中阿斯基-威尔逊多项式是威尔逊多项式的q模拟. (zh)
  • In mathematics, the Askey–Wilson polynomials (or q-Wilson polynomials) are a family of orthogonal polynomials introduced by Askey and Wilson as q-analogs of the Wilson polynomials. They include many of the other orthogonal polynomials in 1 variable as special or limiting cases, described in the Askey scheme. Askey–Wilson polynomials are the special case of Macdonald polynomials (or Koornwinder polynomials) for the non-reduced affine root system of type (C∨1, C1), and their 4 parameters a, b, c, d correspond to the 4 orbits of roots of this root system. They are defined by (en)
  • En mathématiques, les polynômes d'Askey-Wilson (ou q-polynômes de Wilson) sont une famille particulière de polynômes orthogonaux. Ils ont été introduits par Richard Askey et James A. Wilson en 1985, et sont nommés d'après eux. Ces polynômes sont des q-analogues d'une autre famille de polynômes orthogonaux, les (en). (fr)
rdfs:label
  • Askey–Wilson polynomials (en)
  • Polynôme d'Askey-Wilson (fr)
  • Askey–Wilson-polynomen (sv)
  • 阿斯基-威尔逊多项式 (zh)
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