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Abstract and Applied Analysis
Volume 2009, Article ID 168672, 18 pages
Review Article

Exponential Polynomials, Stirling Numbers, and Evaluation of Some Gamma Integrals

Department of Mathematics, Ohio Northern University, Ada, OH 45810, USA

Received 15 May 2009; Accepted 4 August 2009

Academic Editor: Lance Littlejohn

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 Γ ( 𝑎 + 𝑖 𝑡 ) and Γ ( 𝑎 + 𝑖 𝑡 ) Γ ( 𝑏 𝑖 𝑡 ) are evaluated in terms of Stirling numbers.