In mathematics, the Askey-Wilson polynomials are the polynomials <math>p_n(x;a,b,c,d|q) = (ab,ac,ad;q)_na^{-n}\;_{4}\phi_3 \left[\begin{matrix} q^{-n}&abcdq^{n-1}&ae^{i\theta}&ae^{-i\theta} \\ ab&ac&ad \end{matrix} q,q \right] </math> where φ is a basic hypergeometric function and x = cos(&theta) and n is the q-Pochhammer symbol. They were introduced by Askey & Wilson (1985) as q-analogues of the Wilson polynomials.

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  • In mathematics, the Askey-Wilson polynomials are the polynomials <math>p_n(x;a,b,c,d|q) = (ab,ac,ad;q)_na^{-n}\;_{4}\phi_3 \left[\begin{matrix} q^{-n}&abcdq^{n-1}&ae^{i\theta}&ae^{-i\theta} \\ ab&ac&ad \end{matrix} q,q \right] </math> where φ is a basic hypergeometric function and x = cos(&theta) and n is the q-Pochhammer symbol. They were introduced by Askey & Wilson (1985) as q-analogues of the Wilson polynomials.
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  • Askey
  • Wilson
  • 1985 (xsd:integer)
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  • In mathematics, the Askey-Wilson polynomials are the polynomials <math>p_n(x;a,b,c,d|q) = (ab,ac,ad;q)_na^{-n}\;_{4}\phi_3 \left[\begin{matrix} q^{-n}&abcdq^{n-1}&ae^{i\theta}&ae^{-i\theta} \\ ab&ac&ad \end{matrix} q,q \right] </math> where φ is a basic hypergeometric function and x = cos(&theta) and n is the q-Pochhammer symbol. They were introduced by Askey & Wilson (1985) as q-analogues of the Wilson polynomials.
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  • Askey–Wilson polynomials
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