Ismail (1986) gives asymptotic expansions as , with and other parameters fixed, for continuous -ultraspherical, big and little -Jacobi, and Askey–Wilson polynomials. These asymptotic expansions are in fact convergent expansions. For Askey–Wilson the leading term is given by
where with ,
For a uniform asymptotic expansion of the Stieltjes–Wigert polynomials, see Wang and Wong (2006).
For asymptotic approximations to the largest zeros of the -Laguerre and continuous -Hermite polynomials see Chen and Ismail (1998).