The fact that Stirling Numbers of the Second Kind have arisen in various nonrelated fields, from microelectronics to topology, established the need for a more extensive study of the properties of those Stirling numbers. In order to study the properties, new identities and inequalities for Stirling Numbers if the Second Kind must be formed. In an attempt to deepen the understanding of Stirling Numbers, this paper first states and proves known identities and then establishes various new properties through the introduction of additional identities and inequalities.

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http://archive.org/details/propertiesofstir1094515863

Ensign, United States Navy