Abstract and Applied Analysis
Volume 2009 (2009), Article ID 168672, 18 pages
doi:10.1155/2009/168672

Exponential polynomials, Stirling numbers, and evaluation of some gamma integrals

Abstract

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 Γ(a+it) and Γ(a+it)Γ(b−it) are evaluated in terms of Stirling numbers.