Expression and Computation of Generalized Stirling Numbers

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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.
Original languageAmerican English
JournalJournal of Combinatorial Mathematics and Combinatorial Computing
StatePublished - 2013


  • 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.


  • Mathematics

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