Copyright © 2009 Khristo N. Boyadzhiev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.