  Asymptotic approximations for the continuous Hahn polynomials and their zeros
as the degree grows to infinity are established via their three-term recurrence
relation. The methods are based on the uniform asymptotic expansions for
difference equations developed by Wang and Wong (\textit{Numer. Math.}, 2003)
and the matching technique in the complex plane developed by Wang (\textit{J.
Approx. Theory}, 2014).
