§18.29 Asymptotic Approximations for
-Hahn and Askey–Wilson Classes
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
18.29.1
where with
,
18.29.2
;
fixed.
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).

