International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 10, Pages 98175, 10 p.
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
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.