This article is a short elementary review of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of analysis. Some new properties are included, and several analysis-related applications are mentioned. At the end of the paper one application is described in details—certain Fourier integrals involving and are evaluated in terms of Stirling numbers.
"Exponential Polynomials, Stirling Numbers, and Evaluation of Some Gamma Integrals." Abstr. Appl. Anal. 2009 1 - 18, 2009. https://doi.org/10.1155/2009/168672