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##### 1: 18.29 Asymptotic Approximations for $q$-Hahn and Askey–Wilson Classes
###### §18.29 Asymptotic Approximations for $q$-Hahn and Askey–Wilson Classes
Ismail (1986) gives asymptotic expansions as $n\to\infty$, with $x$ and other parameters fixed, for continuous $q$-ultraspherical, big and little $q$-Jacobi, and AskeyWilson polynomials. …For AskeyWilson $p_{n}\left(\cos\theta;a,b,c,d\,|\,q\right)$ the leading term is given by …
Both the AskeyWilson polynomials and the $q$-Racah polynomials can best be described as functions of $z$ (resp. …
18.28.1 $p_{n}(\cos\theta)=p_{n}\left(\cos\theta;a,b,c,d\,|\,q\right)=a^{-n}\sum_{\ell=% 0}^{n}q^{\ell}\left(abq^{\ell},acq^{\ell},adq^{\ell};q\right)_{n-\ell}\*\frac{% \left(q^{-n},abcdq^{n-1};q\right)_{\ell}}{\left(q;q\right)_{\ell}}\prod_{j=0}^% {\ell-1}{(1-2aq^{j}\cos\theta+a^{2}q^{2j})}=a^{-n}\left(ab,ac,ad;q\right)_{n}% \*{{}_{4}\phi_{3}}\left({q^{-n},abcdq^{n-1},ae^{\mathrm{i}\theta},ae^{-\mathrm% {i}\theta}\atop ab,ac,ad};q,q\right).$
For $\omega_{y}$ and $h_{n}$ see Koekoek et al. (2010, Eq. (14.2.2)).
##### 3: 18.1 Notation
• AskeyWilson: $p_{n}\left(x;a,b,c,d\,|\,q\right)$.

• ##### 4: Tom H. Koornwinder
Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of AskeyWilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC. …
• T. H. Koornwinder (1992) Askey-Wilson Polynomials for Root Systems of Type $BC$ . In Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications (Tampa, FL, 1991), Contemp. Math., Vol. 138, pp. 189–204.
In one variable they are essentially ultraspherical, Jacobi, continuous $q$-ultraspherical, or AskeyWilson polynomials. …