# Does the following integrand have an evaluation?

One of the many terms in an equation I have derived has the following:

$\int^{+\infty}_{-\infty} \text{sin}^2\left[a(1+erf(x))\right]H_n(x)\text{exp}(-x^2)dx$

H is the Hermite polynomial and n is an integer. It looks simple enough to have an analytical solution, however I cannot see one. Have look though literature and come up short.

• Mathematica can't solve the case $n=a=1$. Numerically it's a rather pleasing function of $a$ when $n=1$, though. – Patrick Stevens Aug 22 '15 at 21:39