Hermite Polynomials Overlap Integral

[BJ Coste <bc7578@bristol.ac.uk>]

I am presently developping a model for optic fibers where the different
modes of the fiber can be expressed through Hermite Polynomials.

Dr. Griffel from the Mathematic Department of Bristol Univerity
advised me to contact your group.


I am stuck because I would need an analytic formula for a special
integration :

int(-infty,+infty, He(p,ax)*He(q,bx)*exp(-x^2/2),dx)

and the formulas present in the Bateman Manuscript don't really fit.

I guess this kind of theoretical calculation has already been
undertaken.

I would be very grateful your group could help me with finding the
analytic expression.

Best Regards,

Bruno Coste