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.