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).

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