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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.

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

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