2012/10/01 by Khristo N. Boyadzhiev · 1 citation
Mathematics · #History and Theory of Mathematics #Advanced Mathematical Identities #Mathematics and Applications
paper · doi:10.4169/math.mag.85.4.252
openalex publication_date 2012/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
SummaryThis 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, they appear in several differentiation and summation formulas. The reader can also see the connection of S(m, k) to Bernoulli numbers, to Euler polynomials, and to power sums.