Asymptotics of Chebyshev-Stirling and Stirling numbers of the second kind

For the Chebyshev-Stirling numbers, a special case of the Jacobi-Stirling numbers, asymptotic formulae are derived in terms of a local central limit theorem. The underlying probabilistic approach also applies to the classical Stirling numbers of the second kind. Thereby a supplement of the asymptotic analysis for these numbers is established.