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mathematical physics > special function > hypergeometric function > Askey-Wilson polynomial

mathematical analysis > functional analysis > special function > hypergeometric function > Askey-Wilson polynomial

... > function > elementary function > polynomial > orthogonal polynomials > Askey-Wilson polynomial

algebra > polynomial > orthogonal polynomials > Askey-Wilson polynomial

mathematical analysis > combinatorics > q-analog > Askey-Wilson polynomial

algebra > combinatorics > q-analog > Askey-Wilson polynomial

Terme préférentiel

Askey-Wilson polynomial

Définition(s)

In mathematics, the Askey–Wilson polynomials (or q-Wilson polynomials) are a family of orthogonal polynomials introduced by Askey and Wilson (1985) 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 ( $C \lor 1, C 1$ ), and their 4 parameters $a$ , $b$ , $c$ , $d$ correspond to the 4 orbits of roots of this root system.
They are defined by

${\\displaystyle p_{n}(x)=p_{n}(x;a,b,c,d\\mid q):=a^{-n}(ab,ac,ad;q)_{n}\\;_{4}\\phi _{3}\\left[{\egin{matrix}q^{-n}&abcdq^{n-1}&ae^{i\ heta }&ae^{-i\ heta }\\\\ab&ac&ad\\end{matrix}};q,q\ ight]}$

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 $n$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Askey%E2%80%93Wilson_polynomials)

Concept(s) générique(s)

Synonyme(s)

q-Wilson polynomial

Traductions

polynôme d'Askey-Wilson

français
q-polynôme de Wilson

URI

http://data.loterre.fr/ark:/67375/PSR-J4S0TSB9-W

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RDF/XML TURTLE JSON-LD Date de création 27/07/2023, dernière modif. 22/08/2023