Integrals of products of Hermite polynomials

[tommyli]

Hey people,

I need to calculate inner product of two Harmonic oscillator eigenstates with different mass. Does anybody know where I could find a formula for
$\int{ H_n(x) H_m(\alpha x) dx}$

where $H_n, H_m$ are Hermite polynomials?

 

[cgk]

Here, for example:
http://www.wolframalpha.com/input/?i=Integrate[HermiteH[3%2C+x]*HermiteH[5%2C+x%2F3]%2C+x]

(use {x,-Infinity,+Infinity} for the last argument to get a definite integral, although this does not actually converge for this example)