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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 98175, 10 pages
http://dx.doi.org/10.1155/IJMMS/2006/98175

The truncated exponential polynomials, the associated Hermite forms and applications

1ENEA, UTS Tecnologie Fisiche Avanzate, Centro Ricerche Frascati, Via Enrico Fermi 45, Frascati, Rome 00044, Italy
2Dipartimento di Energetica, Università degli Studi di Rome “La Sapienza,”, 14 Via A. Scarfa, Rome 00161, Italy

Received 3 April 2006; Accepted 3 April 2006

Copyright © 2006 Hindawi Publishing Corporation. 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.

Abstract

We discuss the properties of the truncated exponential polynomials and develop the theory of new form of Hermite polynomials, which can be constructed using the truncated exponential as a generating function. We derive their explicit forms and comment on their usefulness in applications, with particular reference to the theory of flattened beams, used in optics.