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Presentation
Asymptotic Expansions and Computation of Generalized Stirling Numbers and Generalized Stirling Functions
International Congress of Mathematicians Coex (2014)
  • Tian-Xiao He, Illinois Wesleyan University
Abstract

Here presented is a unified approach to Stirling numbers and their generalizations as well as generalized Stirling functions by using generalized factorial functions, k-Gamma functions, and generalized divided difference. Previous well-known extensions of Stirling numbers due to Riordan, Carlitz, Howard, Charalambides-Koutras, Gould-Hopper, Hsu-Shiue, Tsylova Todorov, Ahuja-Enneking, and Stirling functions introduced by Butzer and Hauss, Butzer, Kilbas, and Trujilloet and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations and generating functions are discussed. Some asymptotic expansions for the generalized Stirling functions and generalized Stirling numbers are established. In addition, four algorithms for calculating the Stirling numbers based on our generalization are also given.

Disciplines
Publication Date
Summer August 14, 2014
Citation Information
Tian-Xiao He. "Asymptotic Expansions and Computation of Generalized Stirling Numbers and Generalized Stirling Functions" International Congress of Mathematicians Coex (2014)
Available at: http://works.bepress.com/tian_xiao_he/47/