Stirling Numbers

James Stirling (1692-1770), remembered for the Stirling numbers, the Stirling’s interpolation formula, and the formula for the Gamma function among many other things, was one of the great minds of classic numerical analysis. Among Stirling’s goals was to find methods to speed up series convergence. The studies yield interesting number sequences that are now known as Stirling numbers. Stirling numbers have applications in various fields of study, particularly in combinatorial problems. Generalized definitions and implementations for the two types of Stirling numbers are desired. This research focuses on generalized definition, identity, and implementation of Stirling numbers for complex input arguments through contour integration. In addition to exploiting symmetry property, certain representation of the contour integration contributes to a more efficient implementation. This thesis then presents an alternative method for computing both kinds of Stirling numbers.