# A Integral involving Hermite polynomials

1. Feb 18, 2017

### dft5

Hello. I've an integral:
$\int_{-\infty}^{0}x\exp(-x^2)H_n(x-a)H_n(x+a)dx$
Of course for any given $n$ it can be calculated, but I'm interested if there is some general formula for arbitrary $n$. Could someone with access type that into Mathematica? In case that there exists general formula, idea how to derive it would be even better. Thanks in advance.

2. Feb 23, 2017