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Article
Expression and Computation of Generalized Stirling Numbers
Journal of Combinatorial Mathematics and Combinatorial Computing (2013)
  • Tian-Xiao He, Illinois Wesleyan University
Abstract
Here presented is a unified expression of Stirling numbers and their generalizations by using generalized factorial functions and generalized divided difference. Three algorithms for calculating the Stirling numbers and their generalizations based on our unified form are also given, which include a comprehensive algorithm using the characterization of Riordan arrays.
Keywords
  • Stirling numbers of the first kind,
  • Stirling numbers of the second kind,
  • factorial polynomials,
  • generalized factorial,
  • divided difference,
  • k-Gamma functions,
  • Pochhammer symbol and k-Pochhammer symbol.
Disciplines
Publication Date
2013
Publisher Statement
The Journal of Combinatorial Mathematics and Combinatorial is published by The Charles Babbage Research Centre, http://www.combinatorialmath.ca/jcmcc/.
Citation Information
Tian-Xiao He. "Expression and Computation of Generalized Stirling Numbers" Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 86 (2013)
Available at: http://works.bepress.com/tian_xiao_he/52/