Close encounters with the Stirling numbers of the second kind
arXiv:1806.09468
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.
arXiv comment19 pages. This is a modified version of the paper published in the Math Magazine (2012)