Close Encounters with the Stirling Numbers of the Second Kind

  title={Close Encounters with the Stirling Numbers of the Second Kind},
  author={Khristo N. Boyadzhiev},
  journal={Mathematics Magazine},
  pages={252 - 266}
  • K. Boyadzhiev
  • Published 1 October 2012
  • Mathematics
  • Mathematics Magazine
Summary This is a short introduction to the theory of Stirling numbers of the second kind S(m, k) from the point of view of analysis. It is written as an historical survey centered on the representation of these numbers by a certain binomial transform formula. We tell the story of their birth in the book Methodus Differentialis (1730) by James Stirling, and show how they mature in the works of Johann Grünert. The paper demonstrates the usefulness of these numbers in analysis. In particular… 
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