English

Close encounters with the Stirling numbers of the second kind

History and Overview 2018-06-26 v1

Abstract

This is a historical introduction to the theory of Stirling numbers of the second kind S(n,k) from the point of view of analysis. We tell the story of their birth in the book of James Stirling (1730) and show how they mature in the works of Johann Grunert (1843). We demonstrate their usefulness in several differentiation formulas. The reader can also see the connection to Bernoulli numbers, to Euler polynomials and to power sums.

Keywords

Cite

@article{arxiv.1806.09468,
  title  = {Close encounters with the Stirling numbers of the second kind},
  author = {Khristo N. Boyadzhiev},
  journal= {arXiv preprint arXiv:1806.09468},
  year   = {2018}
}

Comments

19 pages. This is a modified version of the paper published in the Math Magazine (2012)