Date of Award


Degree Type


Degree Name

Master of Science


Applied Mathematics


Dr. David J. Jeffrey


Stirling numbers have applications in various fields of study, particularly in combinatorics problems. Generalized definitions and implementations for the two types of Stirling numbers are desired. The 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. Comparison with classical identities and on integer arguments provide a validation of the implementation. This thesis then presents a faster and more efficient method for computing Stirling number of the first type than Maple’s current implementation upon comparison of timing and memory usage.



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