International Journal of Mathematics and Mathematical Sciences 
Volume 2006 (2006), Article ID 98175, 10 pages
doi:10.1155/IJMMS/2006/98175

The truncated exponential polynomials, the associated Hermite forms and applications

G. Dattoli1 and M. Migliorati2

 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

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.