The method of the generating function is exploited to derive analytical expressions of integrals involving products of Hermite polynomials. It is shown that, this type of integrals, often appearing in problems relevant to Free Electron laser or optical radiation confinement can be expressed in terms of generalized Hermite polynomials. The possibility of extending the method to the case of Bessel function is also touched on.
All Science Journal Classification (ASJC) codes
Dattoli, G., Renieri, A., & Torre, A. (1998). Generalized polynomials and derivation of integrals involving products of hermite polynomials. Radiation Physics and Chemistry, 53(4), 391 - 395. https://doi.org/10.1016/S0969-806X(98)00020-6