Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range including the classical integral domain.

Bell and Stirling numbers (msc 11B73), Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (msc 41A60)
CWI
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Chelluri, R, Richmond, L.B, & Temme, N.M. (1999). Asymptotic estimates for generalized Stirling numbers. Modelling, Analysis and Simulation [MAS]. CWI.